Mechanical Behavior of Multi-Channel Tube for HVACR Systems

A thesis presented to

the faculty of

The Russ College of Engineering and Technology of Ohio University

In partial fulfillment

of the requirements for the degree

Master of Science

Lin Qi

December 2013

© 2013 Lin Qi. All Rights Reserved. 2

This thesis titled

Mechanical Behavior of Copper Multi-Channel Tube for HVACR Systems

by

LIN QI

has been approved for

the Department of Mechanical Engineering

and the Russ College of Engineering and Technology by

Frank F. Kraft

Associate Professor of Mechanical Engineering

Dennis Irwin

Dean, Russ College of Engineering and Technology

3

Abstract

QI, LIN, M.S., December 2013, Mechanical Engineering

Mechanical Behavior of Copper Multi-Channel Tube for HVACR Systems

Director of Thesis: Frank F. Kraft

The purpose of this research was to evaluate the mechanical behavior of extruded

(UNS-C12200) copper multi-channel tube for HVACR (heating, ventilation, air conditioning and refrigeration) systems. A model was developed to predict the burst pressure of the copper tube. The assumption for the model is based on plane strain plastic deformation to an instant of instability where differential internal pressure is equal to zero. Physical simulations were used to develop a relevant microstructure that is representative of the tube in a manufactured heat-exchanger. To this end, cold rolling was used to simulate post-extrusion straightening and sizing of the tube. A subsequent thermal treatment was performed in a tube to simulate a thermal cycle.

Tensile tests were conducted to obtain material data, and to determine material constants for a Voce type constitutive equation. Burst tests were conducted to validate the predictive model. Burst pressures were predicted to within 6% of measured values. The effects from cold working and the simulated brazing cycle were also evaluated in this research.

4

Acknowledgements

I would like to thank Dr. Frank Kraft for his guidance on this research, in the metallurgy and metal forming classes. Under his guidance, I learned how to do research perfectly. He taught me a motivated attitude for the research and work for my future career and life. I would also like to thank Dr. Hajrudin Pasic. He gave me a lot of valuable suggestions during my research process. He also taught me about how to adapt to the study life at Ohio University. I would also like to thank Dr. John Cotton. He gave me a lot of important feedback on my research. He introduced many good software to

ME students in the computer lab. I would also like to thank Dr. Todd Young for his patience to be my committee member. I also want to thank Randy Mulford for his effort on manufacturing several parts of the test station. I want to thank all of the faculty from mechanical engineering department for their earnest teachings.

I enjoyed my three years of academic life in this beautiful country. I appreciate the help and friendship from American people.

In the end, I would like to thank my parents, Yong and Lili, for their generous support. 5

Table of Contents

Page

Abstract ...... 3 Acknowledgements ...... 4 List of Tables ...... 7 List of Figures ...... 8 Chapter 1 Introduction ...... 10 1.1 Material ...... 11 1.3 Processing of Hot Extruded of Aluminum Tube ...... 13 1.4 Nocolok® brazing of Aluminum Heat Exchangers ...... 13 1.5 Change in Properties during Brazing ...... 14 1.6 Copper Extrusion...... 16 1.7 Brazing Process ...... 16 Chapter 2 Objectives ...... 18 Chapter 3 Analytical Model ...... 20 3.1 The Effective Stress and Strain ...... 21 3.2 Constitutive Equation ...... 24 3.3 Instability Analysis ...... 25 Chapter 4 Experimental Approach...... 32 4.1 Cold Rolling ...... 32 4.2 Brazing Simulation ...... 33 4.3 Tensile Testing ...... 36 4.3.1 Preparation Work for the Test ...... 36 4.3.2 Uncertainty of the Cross-Section Area ...... 38 4.3.3 Geometry of the Samples ...... 39 4.3.4 Tensile Testing Procedure ...... 39 4.4 Pressure Testing ...... 41 4.4.1 Test Apparatus ...... 42 6

4.4.2 Experimental Set-up ...... 43 Chapter 5 Results and Discussion ...... 48 5.1 Tensile Testing Results ...... 48 5.1.1 As-Extruded Tubes ...... 48 5.1.2 Cold Rolled Tubes ...... 51 5.1.3 Rolled and Heat Treated Tubes ...... 53 5.1.4 The Effect of Cold Rolling and Heat Treatment Process on Uniaxial Tension Test ...... 56 5.2 Pressure Testing Results...... 58 5.2.1 As-Extruded Tubes ...... 58 5.2.2 Cold Rolled Tubes ...... 60 5.2.3 Rolled and Heat Treated Tubes ...... 61 5.2.4 The Effect of Cold Rolling and Heat Treatment Process on the Pressure Test 62 5.2.5 Tube Failure ...... 65 5.3 Microstructure Results ...... 68 5.4 Burst Models ...... 71 5.4.1 Miller and Kraft Model ...... 71 5.4.2 New Model ...... 73 Chapter 6 Conclusions ...... 78 6.1 Summary and Conclusions ...... 78 6.2 Future Work ...... 80 References ...... 81 Appendix: Initial Dimensions of the Cross-Section ...... 85

7

List of Tables

Page

Table 4.1: Initial measurement of tensile test samples……………………………...... 38 Table 4.2: Uncertainty of , length and mass…………………………………….39 Table 5.1: Comparison of results from uniaxial tensile testing………………………...58 Table 5.2: Burst pressure results of the as-extruded tubes……………………………..60 Table 5.3: Burst pressure results of the cold rolled tubes………………………………61 Table 5.4: Burst pressure results of the rolled-heat treated tubes………………………62 Table 5.5: Burst pressure results of an as-extruded sample, a cold rolled sample, and a rolled-heat treated sample……………………………………………………………….65 Table 5.6: Instability strains of pressurized samples predicted by Kraft and Miller model…………………………………………………………………………………….72 Table 5.7: Pressure test results and Kraft-Miller model predictions……………………72 Table 5.8: Instability strains of pressurized samples predicted by the new model...... 74 Table 5.9: Pressure test results and new model predictions…………………………….75 8

List of Figures

Page

Figure 1.1: All-copper heat exchanger [11]…………………………………………….11 Figure 1.2: Copper multi-channel profiles produced at Ohio University [11]………….12 Figure1.3: Aluminum heat exchanger with headers, fins and tubes [15]……………….14 Figure 1.4: AA3102 aluminum multi-channel tube in pre-braze condition [18]…….....15 Figure 1.5: AA3102 aluminum multi-channel tube in post-braze condition [18]……….15 Figure 3.1: Figure (a) is the illustration of a section of tube, with internal pressure (P) and principal stresses ( ). Figure (b) shows the balance of forces in the internal wall ( ) with that imposed in the adjacent channels (WlP)………………………….21 Figure 3.2: Comparison between two instability criterions……………………………...29 Figure 3.3: Applying the Voce equation into instability criterion (Equation 34) from this research, the instability strain is predicted as a function of ratio between web thicknesses and void width. Applying the same Voce equation into Kraft-Miller instability criterion (Equation 32), the instability strain from the prediction is a constant value………………………………………………………………………….31 Figure 4.1: Laboratory rolling mill……………………………………………………...33 Figure 4.2: Two cold rolled samples are loaded into tube holder………………………34 Figure 4.3: The control panel………………………………………………35 Figure 4.4: Brazing simulation on UNS 122000 copper tube samples………………….36 Figure 4.5: Sketch of the copper multi-channel tube profile…………………………….37 Figure 4.6: Instron® 5567 tensile testing ………………………………………40 Figure 4.7: MTS machine and testing station……………………………………………42 Figure 4.8: Test apparatus……………………………………………………………….43 Figure 4.9: Experimental set-up in burst testing………………………………………...44 Figure 4.10: Fluid reservoir and charge tank……………………………………………45 Figure 4.11: Procedure of the burst test…………………………………………………46 Figure 5.1: Tensile testing data for three as-extruded samples fitted with equation…………………………………………………………………………………..48 Figure 5.2: Tensile instability strain in the as-extruded tubes predicted by applying Voce equation…………………………………………………………………………………..50 Figure 5.3: Tensile testing data for 2 cold rolled samples fitted with equation…...51 Figure 5.4: Tensile instability strain in the cold rolled tubes predicted by applying Voce equation…………………………………………………………………………………..52 9

Figure 5.5: Tensile testing data for 2 cold rolled, heat treated samples fitted with equation………………………………………………………………………………….54 Figure 5.6: Tensile instability strain in the heat treated tubes predicted by applying Voce equation………………………………………………………………………………….55 Figure 5.7: Uniaxial strain-stress curves of samples in three different conditions……..52 Figure 5.8: Pressure testing data for three as-extruded samples………………………..59 Figure 5.9: Pressure testing data for 3 cold rolled samples……………………………..60 Figure 5.10: Pressure testing data for 3 rolled and heat treated samples………………..62 Figure 5.11: Comparison of test pressure-ram displacement of an as-extruded sample, a cold rolled sample, and a rolled-heat treated sample…………………………………….64 Figure 5.12: External feature of the first type of tube failure………...... 66 Figure 5.13: External feature of the second type of tube failure………………………..67 Figure 5.14: External feature of the third type of tube failure…………………………..68 Figure 5.15: UNS 122000 copper multi-channel tube in as-extruded condition………..70 Figure 5.16: UNS 122000 copper multi-channel tube in cold rolled condition…………70 Figure 5.17: UNS 122000 copper multi-channel tube in rolled-heat treated condition…71

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Chapter 1 Introduction

High efficiency heat exchangers used in the HVACR (heating, ventilation, air conditioning and refrigeration) frequently consist of multi-channel tubes and fins combined between two headers [1]. The header receives the refrigerant and distributes passage of it into the tubes. A simple prototype of an all-copper heat exchanger using this type of construction is shown in Figure 1.1. The refrigerant flows within the multiple internal tube channels. A relatively large surface area of contact between the refrigerant and tubing per volume of refrigerant is ensured by the use of the multi-channel tube.

Currently, multi-channel tube heat exchangers are only commercially available in aluminum alloys, largely due to the ease of manufacture. A process to produce copper multi-channel tubes have been developed by researchers at Ohio University [2–4].

Presently, the refrigerant used in automotive refrigeration is primarily R134a. For residential and commercial cooling systems, R410a is now the predominant refrigerant used [5]. There also has been some renewed interest in carbon dioxide (R744a) as a refrigerant [6]. The R744 system operates at a greater pressure and temperature compared to an R134a system. The maximum pressure of an R744 system is 18MPa and the maximum operating temperature is 180 ℃ [7,8]. It is important to predict the burst pressure and failure strain for such applications.

The principal objective of this research is to generate a predictive model to predict the failure pressure of the tube. The material data to make the predictions will come from 11 basic tensile testing. Validation of the predictive model will be based on pressure tests to tube failure.

1.1 Material

The tube material’s designation is UNS 122000 (or CDA-122 DHP) copper. This copper is typically used in condenser tubes, evaporator tubes and heat exchanger tubes.

This material has high residual phosphorus, which is used to deoxidize it. The composition of it is 99.9% Cu and .015-.040 % P [9]. This material’s suitability level of and brazing is excellent. The hot and cold workability of this material is also very good [10]. Figure 1.2 shows examples of copper multi-channel tubes produced at

Ohio University.

Figure 1.1: All-copper heat exchanger [11].

12

1.2 Advantages of Copper

Copper has a number of desirable characteristics for heat exchanger applications.

Copper has a higher strength compared to the typical aluminum alloys used in such applications. The of the copper is 398W/(mK) while the thermal conductivity of the aluminum is only 247 W/(mK) [12]. The working temperature of copper alloys is also higher than aluminum. Brazing and soldering joining operations is also easier to accomplish on copper. The exceptional resistance of copper alloys is another advantage for the usage of this material. On the hygiene side, copper has antimicrobial properties which can inhibit mold growth. It is also difficult for bacteria and microorganisms to survive on copper [13].

Figure 1.2: Copper multi-channel profiles produced at Ohio University [11]. 13

1.3 Processing of Hot Extruded of Aluminum Tube

Copper multi-channel tubes are expected to be produced and fabricated into heat exchangers in a somewhat similar manner to that of aluminum tubes. For this reason, processing of aluminum multi-channel tubes and heat exchangers is briefly reviewed here. Currently, AA 1000 and AA 3000 series alloys are used in the production of multi- channel tubes [3]. In order to create the uniform cross section geometry of the tube, a hot extrusion process is used in the manufacturing process [1]. Miller [1] reviewed the hot extrusion process of the aluminum tube. Essentially, a heated aluminum alloy billet is placed into a container, from which a hydraulic ram pushes it through a die. Because very precise outer dimensions of the multi-channel tubing are necessary in heat exchanger furnace brazing, the tube is straightened, roll-sized and cut to a final length after extrusion. The tubes are then assembled into heat exchangers. The straightening and roll-sizing processes impose a small amount of cold-work (or plastic strain) on the tube [7]. This process makes roughly a 3-7% thickness reduction on the tube [14].

1.4 Nocolok® brazing of Aluminum Heat Exchangers

During fabrication of the aluminum heat exchanger, the assembly undergoes

Nocolok® furnace brazing [1]. The tubes are brazed to the headers and the fins are brazed to the tubes [1]. Figure 1.3 shows a photo of an aluminum heat exchanger with individual components identified.

14

Figure 1.3: Aluminum heat exchanger with headers, fins and tubes [15].

The brazing alloy is between the components to be joined [16], and in this case it is usually clad onto the header and fin-stock material. The whole assembly is heated to a temperature at which the brazing flux and alloy will melt. The tube alloy does not melt because it has a higher melting point than the brazing alloy [7]. Metallurgical bonds are formed between the joining surfaces of the components by the brazing alloy [16]. The brazing process is performed inside a furnace with a nitrogen atmosphere. The operating temperature of the brazing process ranges from 600-605 °C [1].

1.5 Change in Properties during Brazing

Guzowski, et al. [17] have shown that recrystallization and grain growth occurs during the brazing cycle and this is attributed to the prior cold work induced in the straightening and roll-sizing process. Figures 1.4 and 1.5 show the grain size growth phenomenon on the AA 3102 aluminum multi-channel tube before and after the brazing 15 process. The cold work in the straightening and roll-sizing process is from a 3-7% thickness reduction on the tube [18].

Figure 1.4: AA3102 aluminum multi-channel tube in pre-braze condition [18].

Figure 1.5: AA3102 aluminum multi-channel tube in post-braze condition [18]. 16

The grain growth that occurs in the internal walls of the tube during the brazing cycle reduces the strength and ductility of the sample [1]. Vamadevan [7] compared the failure pressure of AA 3102 aluminum multi-channel tubes before and after the brazing cycle. The tube’s failure pressure decreased by 17% after the brazing cycle. Kraft and

Williams [14] showed that the larger grain size after the brazing cycle caused a 22% reduction in failure pressure of AA 3102 aluminum tube when the tube thickness had a

3% thickness reduction.

1.6 Copper Extrusion

The straight uniform cross section of the copper multi-channel tube is also produced by a hot extrusion process. Kraft [3] has published a patent for a unique multi-billet extrusion process to produce this tube. In this process, two heated billets are inserted into a container of the extrusion press. The billets are simultaneously pushed into a die by a high ram force and extruded to form top and bottom portions that combine to make the tube [3]. A solid state weld joins the top half to the bottom half to form the multi-channel tube in the die [3,19]. After extrusion, the tube would be expected to pass through a series of rollers to be straightened and sized, similar to what occurs with aluminum tubes.

The effect of such processing on recrystallization and grain growth in the copper tube during brazing is to be determined as part of this research.

1.7 Brazing Process

Similar to the aluminum heat exchanger processing, the straightened and roll-sized copper tubes will also be subject to furnace brazing. The atmosphere of the copper brazing process is usually nitrogen-based, often up to 15% hydrogen. The typical copper 17 furnace brazing process has the trade name, CuproBraze® [20]. The brazing process uses a CuSnNiP filler metal alloy and nitrogen based controlled atmosphere furnace. The brazing temperature should reach 650℃ for 2-3 minutes [20]. Subsequently, the material is cooled to room temperature. The photo of a prototype CuproBrazed all copper heat exchanger is shown in Figure 1.1.

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Chapter 2 Objectives

The main goal of this research was to develop an analytical model to predict the mechanical response and failure pressure of copper multi-channel tube for HVACR systems. The material data to make the predictions was from basic tensile testing.

Pressure tests were conducted in order to validate the model. Listed below are the main objectives, some basic methods to accomplish the research, and secondary objectives.

The specific objectives were:

 To develop a suitable analytical model for multi-channel copper tubes in order to

predict failure pressure.

o This predictive model expresses the failure pressure in terms of the

instability strain, initial dimensions of the multi-channel tube and material

constants.

o The assumption for the model is listed below

o Rectangular channels in the tube

o Plane strain plastic deformation

o Initial failure occurs at the internal walls and this coincides with

the maximum pressure

 To evaluate material behavior before straightening, roll-sizing and brazing.

o Use tensile testing to develop constitutive equation

o Perform pressure tests to validate the predictive model 19

 To evaluate material behavior after straightened and roll-sized condition, but

before brazing. Tensile tests were used to generate the constitutive equation, and

pressure tests were correlated to the model.

 To evaluate material behavior after straightening, roll-sizing and brazing

o The copper brazing process was simulated on tube samples with a lab

furnace

o Tensile and pressure tests were performed to determine a suitable

constitutive equation and correlate pressure test data, respectively.

 To evaluate the effect from the cold work and brazing cycle

o To quantify the cold work’s effect on the mechanical properties of tubes.

o To compare the microstructure and grain size before and after the brazing

cycle.

o To assess the effect of brazing on the mechanical properties of tubes.

20

Chapter 3 Analytical Model

As the refrigerant flows through the heat exchanger, the multi-channel tube must withstand the internal pressure [1]. Mechanical failure is an important issue which should be considered by the designer. It is imperative to predict the instability strain and failure pressure of the tubes.

Several predictive models have already been proposed by previous researchers.

Vamadevan [7] has shown that the maximum pressure occurs at the internal wall (the web) between two adjacent channels by using a finite element analysis. Künesch [21] considered the multi-channel tubing as a series of individual tubes. A formula for the effective stress at the web was derived by superimposing the pressures exerted on the two sides of the internal wall (web).

Kraft and Miller [18] simplified this mechanical failure problem to a plane strain thin wall tube problem, for a tube with round channels. The analysis was then applied to rectangular channels tube. They defined the differential strain in the principal 1 (hoop) direction (of an internal wall) as the change in the channel diameter with respect to diameter. This assumption is not made in this thesis since an analysis based on square channels is derived.

Kraft and Jamison [22] applied the Hollomon and Voce material models to predict the failure pressure in round copper tubes. An instability analysis was used to predict the failure pressure in terms of the initial dimensions of the tubing and constants of the constitutive equation. The constants of the constitutive equation can be determined from the basic tensile test. 21

3.1 The Effective Stress and Strain

For typical tube designs, the maximum internal pressure is achieved just prior to failure of an internal wall. A tube fails or bursts after one or more internal walls fail [7].

Thus, analysis of the stress and strain state will focus on the internal wall. The literature presents such analyses for circular and rectangular channels [1,7,18,23,24], and these are reviewed here. They provide the basis for the model developed in this thesis. The stress acting on an internal wall is depicted in Figure 3.1.

(a) (b)

Figure 3.1: Figure (a) is the illustration of a section of tube, with internal pressure (P) and principal stresses ( ). Figure (b) shows the balance of forces in the internal wall

( ) with that imposed in the adjacent channels (WlP).

Figure 3.1shows the stress state in an internal wall of a multi-channel tube. The width of the channel is defined as ; The thickness of the wall is defined as ; The internal pressure is defined as ; and the length of the tube is defined as . The height of the channel is defined as . 22

For a static analysis, the net force in the vertical direction ( ) is zero and this leads to Equation 2.

∑ (1)

( ) (2)

The principal stresses and are given in Equations 3 and 4 [1,7,23].

(3)

(4)

is the principal strain in the longitudinal direction. Plane strain is assumed for this analysis such that there is no longitudinal strain during plastic deformation.

(5)

is defined as the differential strain in the longitudinal direction.

By applying the Levy-Mises equation [25], the 2 principal stresses can be determined.

̅

̅ (6)

̅ and ̅ are the effective stress and strain, respectively.

The longitudinal stress is thus expressed in Equation 7.

(7)

The effective (or von Mises) stress ( ̅) is given in Equation 8 [25].

̅ (8) √ 23

Substituting Equation 7 into Equation 8, the effective stress can be expressed as follows

[1].

̅ √ (9)

Substituting Equations 3 and 4 into Equation 9, the effective stress can be expressed in terms of pressure, channel width and the thickness of the internal wall.

Equation 10 has also been presented in the literature for circular channels [1,7,18].

̅ √ ( ) (10)

Since volume is constant during plastic deformation, the principal strains in the internal walls can be further defined in Equations 11 and 12.

(11)

(12)

is the initial height of the channel. While is the initial thickness of the internal wall. is the incremental change in wall thickness. is the incremental change in channel width. The principal strains and in an internal wall can also be expressed as follows [1,23].

(13)

(14)

(15)

(16)

The effective plastic strain ( )̅ is given in Equation 17 [25]. 24

̅ [ ] (17)

Substituting Equation 12, 15 and 16 into the Equation 17, effective strain can be expressed in terms of wall thickness.

̅ | | (18) √

3.2 Constitutive Equation

Constitutive equations describe a relation between the true (effective) stress and strain. The tensile test is a good way to obtain data to determine material constants of a constitutive equation. The true stress and strain in uniaxial tensile are effective strain and stress [22].

The Voce equation is reported to be a superior constitutive equation when evaluating the strain hardening behavior of copper [26]. From the form of Tiryakioglu and Voce [27,28], the Voce equation is:

̅ ̅ (19)

, and are material constants. By substituting Equation 10 into Equation 19, the tube pressure can be expressed in terms of the channel width, internal wall thickness, the material constants and the effective strain.

̅ (20) √

Kraft and Jamison [22] stated that two criteria should be satisfied for an accurate model. Firstly, the constitutive model should be highly correlated to the true stress-strain data from the tensile test. Secondly, the instability strain determined for uniaxial tension 25 with the constitutive equation parameters should closely coincide with actual data from a tensile test. The validation and discussion about this model is discussed in the chapter 5.

3.3 Instability Analysis

Plastic instability of an internal wall, in plane strain, is taken to coincide with the point of maximum pressure (at failure). This analysis examines the instability which occurs in the multi-channel tube under the internal pressure [1]. Instability can be the beginning of localized deformation which leads to burst of the tube [22]. For this effort, the instability point is defined as the instant where the change in the pressure (dP) is zero.

Differentiating P in Equation 3 with respect to the other terms and equating it to zero is performed in Equation 21. This is done to mathematically define the instability point.

(21)

Multiplying both sides of Equation 21 by provides simplification to Equation

22.

(22)

The longitudinal (or axial) strain of the tube is zero, so the area of the deformed internal wall is constant. This is consistent with Equation 12.

(23)

(24)

The deformation of the channel width is related to the deformation of the internal wall thickness. In the beginning, an assumption is made that . But this 26 relation yields a poor predictive model. In order to obtain the ratio between and , a stereomicroscope was used to measure the dimensions of a failed and untested tube.

However overall ratios of dW and – varied from 1 to 3. This method failed to obtain a constant ratio.

It’s important to calculate a constant theoretical ratio during the plastic deformation. Since Miller (and Kraft) [1] developed a predictive model, the ratio could be calculated based on this model. By substituting the pressure test data into this model,

the ratio (f) is obtained as 5.

This ratio can be combined with Equation 24 to express dw as a function of t and h.

(25)

Substituting Equation 25 into the Equation 22 yields:

(26)

Substituting d1 and d3 (=-d1) for dh/h and dt/t, respectively, gives a simpler form of the instability criterion.

( ) (27)

Since W = , ( ⁄√ ) ̅, ( ⁄√ ) ̅,

√ (√ ⁄ ) ̅ ⁄ ( ̅) and , then the instability criterion can be written as a function of initial dimensions and effective stress and strain.

̅ √ ̅{ } (28) ̅ [ ( √ ̅ )]

27

Using an appropriate constitutive equation with Equation 28, the instability strain

̅ can be calculated numerically.

Substituting ̅ into Equation 20, can be expressed in terms of initial dimensions, instability strain, and the material constants of the Voce equation. This is given in Equation 29.

√ ̅ ( ̅ )

√ [ ( ̅ ) ] √

(29)

Equations 29 can be used to determine the maximum pressure in terms of the initial dimensions of the tube, the material constants of the constitutive equation, the dimension factor and the instability strain. These two equations will be assessed as the predictive model for the copper multi-channel tube. Determination of initial dimensions will be presented in the chapter 4. Constitutive equations will be determined via tensile testing as presented in the chapter 4.

As stated previously, Miller and Kraft [1] developed a predictive model for multi- channel tubes. Since that model analyzes tubes with circular channel, it derives a different expression of . It is shown in Equation 30.

(30)

D is the diameter of the circular channel. and . .

Then Equation 30 can be simplified. 28

(31)

Equation 31 can be transformed to a simplified instability criterion by Kraft and Miller

[18].

This criterion is shown in Equation 32.

̅ ̅ √ ̅ (32)

Substituting the constitutive equation into this criterion, the tube instability strain

( ̅ ) can be calculated numerically.

The Miller and Kraft predictive model expresses in terms of initial dimensions, instability strain, and the effective stress. This is given in Equation 33.

̅ ( ) (33) √ (√ ̅ )

The predictive model derived in this research is compared with the predictive model of Miller in Chapter 5.

Substituting the Voce equation from the research of Kraft and Jamison [22] into the instability criterion of Miller’s model, the instability criterion curve has an intersection with the stress-strain curve at 0.22 strain, as shown in Figure 3.2. The internal wall of the tube is essentially predicted to fail at this strain. Substituting the same Voce equation and the same dimension data into the instability criterion in this research (Equation 28), the instability criterion is ̅ ̅ ̅. This criterion also has an intersection with the stress-strain curve at 0.24 strain. The instability strains predicted by two different instability criterions are very close (within 9.1%). The maximum pressure predicted by two different models are within 1.6%.

29

Figure 3.2: Comparison between two instability criterions.

Equation 28 can be simplified by dividing the upper and bottom parts of Equation by and express the ratio between and as .

̅ √ ̅{ }. (34) ̅ [ ( √ ̅ )]

It shows that the instability strain is dependent on the ratio of the internal wall thickness to the channel width. Applying the Voce equation

from the research of Kraft and Jamison [22] into Equation 28, the instability strain at each ratio can be calculated. In Figure 3.3, there are three curves which demonstrate the relation between the (t/W) ratio and the instability strain. Three 30 different curves correlate with different channel width and same ranges of wall thickness.

These three curves are exactly congruent. As the ratio between the wall thickness and channel width increases, the instability strain will decrease. Figure 3.3 show that instability strain predicted by the model in this research is dependent on the ratio of the wall thickness to the channel width. Applying the Voce equation

into Kraft-Miller instability criterion (Equation 32), the instability strain is not dependent on the (t/W) ratio.

31

Figure 3.3: Applying the Voce equation into instability criterion (Equation 34) from this research, the instability strain is predicted as a

function of ratio between web thicknesses and void width. Applying the same Voce

equation into Kraft-Miller instability criterion (Equation 32), the instability strain from

the prediction is a constant value.

32

Chapter 4 Experimental Approach

4.1 Cold Rolling

In a similar manner to aluminum multi-channel tube production, it is anticipated that copper multichannel tube will also need to be straightened and sized after extrusion.

The tube passes between a series of rollers to be straightened. Then the straight tube undergoes the roll-sizing process to obtain precise overall height and width dimensions.

“Cold work” (plastic strain) is imposed on the tube during this process. For this research, a cold rolling process was used to simulate the straightening and sizing process. As shown in Figure 4.1, a laboratory rolling mill was the apparatus used to conduct this process. Samples were roll sized to approximately 5% thickness reduction for this experimental work. The initial average thickness (1.963 mm) of the tube was measured with a micrometer. In order to achieve a 5% thickness reduction, a feeler thickness gage was used to adjust the gap between rollers. The average tube thickness was 1.860 mm after the rolling process, which is a thickness reduction of 5.16%. 33

Figure 4.1: Laboratory rolling mill.

4.2 Brazing Simulation

The CuproBraze [20] process is considered here as the process by which heat exchangers with these tubes are made. In this process, copper heat exchangers are brazed at 650℃ in a furnace, for approximately 2 – 3 minutes. In this research, the brazing thermal cycle was simulated in copper tube samples with a tube furnace using a nitrogen atmosphere. Brazing simulations were performed on as-extruded samples that were cold 34 rolled as described in the previous section. A Lindberg Blue M tube furnace was used to conduct this brazing simulation. As shown in Figure 4.2, thermocouples were placed in close proximity to the tubes, to control and monitor the temperature.

Figure 4.2: Two cold rolled samples are loaded into tube holder.

After the tube holder with samples was placed inside the tube furnace, the temperature controllers were adjusted to 650 ℃ (as shown in Figure 4.3). Prior to heating, the quartz furnace tube was evacuated with a vacuum pump and back-filled with nitrogen gas. The nitrogen gas was allowed to flow through the furnace at a very low flow rate throughout the heating operation.

35

Figure 4.3: The temperature control panel.

The thermocouple temperature was monitored on the computer screen and recorded with a data acquisition module. It took around 10 minutes to reach 650 ℃. The sample was held at that temperature for 2 minutes. At that point, the furnace was turned- off and the sample holder was pushed from the heated zone of the furnace and allowed to cool in the nitrogen atmosphere. Figure 4.4 displays the temperature change over time on the samples during the heat treatment process.

36

Figure 4.4: Brazing simulation on UNS 122000 copper tube samples.

4.3 Tensile Testing

4.3.1 Preparation Work for the Test

As mentioned earlier in this thesis, determination of the constitutive equation is needed to predict the failure pressure of the tubing. Tensile testing of tube samples was used to determine the constitutive equation. Figure 4.5 is a sketch of the copper tube profile and the nominal dimensions.

37

Figure 4.5: Sketch of the copper multi-channel tube profile.

The samples in this research were produced by Barkley [29] and Kochis [30].

Tube from three extrusion trials was used. A limited amount of tube was available and each length of tube was about 1.36 meters. They were labeled as tube no.1, tube no.2 and tube no.3. These numbers indicates the three different extrusion trials used to produce the tube samples. The tubes were extruded from UNS 122000 copper. Tube was cold rolled to achieve about a 5% thickness reduction, to simulate cold work expected during a production sizing/straightening operation. Several cold rolled samples were heat treated in the tube furnace to simulate a production furnace brazing operation. Individual test samples were cut to 165mm (6.5 inches) in length. This provided for a 102 mm (4 inches) distance between the two jaws of the tensile tester. An initial measurement of the sample cross-sectional area for each test sample was performed prior to testing. The 38 tube mass and length were measured with a digital laboratory scale and digital calipers, respectively.

The initial cross-section area was calculated with Equation 35.

(35)

is mass, is tube axial length and is density. The density value for UNS

122000 copper is 8940Kg/m3 [9]. The measurements of as-extruded samples are shown in Table 4.1.

Table 4.1: Initial measurement of tensile test samples.

Tube Sample Mass(g) Length(mm) Area( ) Tube no.1 1 19.32 164.8 13.11 Tube no.2 2 19.55 165.1 13.24 Tube no.3 3 18.71 165.2 12.67 Tube no.3 4 18.54 164.9 12.60 Tube no.3 5 18.49 164.5 12.57 Tube no.3 6 18.49 164.8 12.55 Tube no.3 7 18.59 164.9 12.60

4.3.2 Uncertainty of the Cross-Section Area

To assess the method employed to determine the initial cross-section area of the test samples, an uncertainty analysis was performed [1]. Equation 36 [1] was used to calculate the relative uncertainty. The values of mass, length and density of the sample are associated with the relative uncertainty of the area. The square of their relative uncertainty is summed, and then the square root of their sum is calculated.

[( ) ( ) ( ) ] (36) 39

is the uncertainty of the cross-section area. is the uncertainty of density, is the uncertainty of length. is the uncertainty of mass. These values are presented in Table

4.2.

Table 4.2: Uncertainty of density, length and mass.

Substituting these data into Equation 36, the relative uncertainty in cross-section area was calculated to be 0.14%.

4.3.3 Geometry of the Samples

Samples were metallurgically prepared and measured with a stereomicroscope to determine internal wall and channel dimensions for the analysis of pressure test results.

The dimensions of internal wall thickness and channel width are shown in Appendix

Table A1-A6. The ratios of internal wall thickness to channel width are also presented.

The smallest ratio indicates the worst case (highest stressed wall for a given pressure) for the tube. The ratio in the worst case is chosen to be used to predict the failure pressure of the tube. After cold rolling, this ratio increased by 1.7%-3.3%.

4.3.4 Tensile Testing Procedure

An Instron® 5567 tensile testing machine was used to perform these tests [22].

This instrument is shown in Figure 4.6. A 1 inch (25.4mm) extensometer was used to determine true strain until uniaxial instability. The 165 mm (6.5 inches) sample was loaded into the upper jaw first. Then the extensometer was attached to the center of the 40 specimen. The machine force and extensometer were zeroed prior to tightening of the lower jaw onto the specimen. The test is performed until the maximum force, and hence tensile instability, is exceeded. The test is manually stopped and the extensometer removed from the tube specimen. This is to protect the extensometer from the shock of tube fracture. The recorded force and extensometer data to the instability point

(maximum force) were used to determine the true stress, true strain behavior of the material.

Figure 4.6: Instron® 5567 tensile testing machine.

The machine velocity was programmed to provide an initial strain rate of approximately 10-2 s-1. Equation 37 was used to calculate the cross-head velocity.

41

̇ (37)

is the distance from the upper jaw to the lower jaw. Based on the standard from ASTM E 8 [31], this distance should be 102 mm (~4 inches). is the cross-head velocity of the machine. Using the strain rate of 10-2 s-1 and a distance of 101.6 mm and

Eq. (36), the cross-head velocity is 1.02 mm/sec (0.04 in/sec). Equation 38 is used to calculate the true strain [22].

̅ ( ) (38)

̅ is the true strain. is the length change and the is the distance (25.4 mm) between the edges of the extensometer. The extensometer is used to measure .

The true (plastic) stress was calculated with Equation 39 [22].

̅ (39)

̅ is the true stress. F is the force measured with the load cell. A is the actual cross- section area of the sample. is the initial cross-section area. Since the volume is

constant during the plastic deformation, . Then and , and

Eq. (39) can be generated. A Voce constitutive model was then applied to the data and evaluated in this research.

4.4 Pressure Testing

Miller [1] implemented burst testing to validate a predictive model from constitutive equations determined with tensile testing. An MTS 810 type machine connected to a test station is the apparatus to conduct the experiments. This is shown in 42

Figure 4.7. This apparatus applies fluid pressure to the inside of multi-channel tube samples [1].

Figure 4.7: MTS machine and testing station.

4.4.1 Test Apparatus

The computer-controlled servo hydraulic MTS machine compresses the piston of a high pressure cylinder between the crosshead and ram [1]. The fluid (water+rust- inhibitor) inside this cylinder is pressurized in this process. This process generates the fluid pressure for the test. This pressure is developed in the tube sample, which is gripped with burst test fixtures shown in Figure 4.8. The internal pressure is measured 43 with a pressure transducer. The apparatus can achieve test pressures up to 69 MPa

(10,000 psi).

Figure 4.8: Test apparatus.

4.4.2 Experimental Set-up

The experimental set-up for the pressure test is shown in the Figure 4.9. 44

Figure 4.9: Experimental set-up in burst testing.

Testing was similar to that of Miller [1]. Initially, the sample was loaded into the test fixtures. The charge tank, as seen in Figure 4.10, was then filled with water and then pressurized. The air in the system was evacuated by adjusting the two ball valves as shown in Figure 4.9. 45

Figure 4.10: Fluid reservoir and charge tank.

The burst test procedure was performed on the sample according to settings entered into the MTS software. Figure 4.11 shows a representative screen of the object- oriented MTS (MPT) program used in testing. 46

Figure 4.11: Procedure of the burst test.

In Figure 4.11, “process1” invokes and defines data acquisition, which was sampled at a rate of 0.01 second. Data recorded were time, machine displacement, machine force and pressure.

The “process2” command icon effectively applies 1.4 MPa (200 psi) to the sample in 20 seconds. This was done to quickly load the sample to a low level of pressure to shorten overall test time. The “process3” command holds the sample at this pressure 5 seconds.

The “process4” command pressurizes the sample to failure or burst. The rate of the ram speed is 1.27 mm/sec (0.05 in/sec) during this process. Since the area of the 47 ram’s hydraulic cylinder is 645 (1 ), the flow rate of the ram was calculated as approximately 819 /sec (0.05 /sec).

The burst tests were conducted with three different groups of samples. The first group of samples (three samples) was in the as-extruded condition without rolling reduction. The second group of samples (four samples) was as-extruded and cold rolled to a 5% thickness reduction. The third group of samples (four samples) was as -extruded, cold rolled for 5% thickness reduction, and heat treated (simulated brazing) at 650 ℃ for

2 minutes.

4.5 Metallography

In order to determine the effect from the cold work and brazing cycle, metallography was required to view the microstructure of the sample. This polishing process is similar to that of Williams [32]. A short tube sample was mounted in epoxy and polished with the following procedure. The sample was ground with 180, 320 and

600 grit SiC paper, and in this sequence. Final polishing was with 6 m and 1 m diamond. Then, the sample was etched with 25 ml , 25 ml and 50 ml of 3%

, for 10 seconds. The microstructures were inspected under a Nikon microscope.

Analysis of the microstructure is presented in chapter 5.

48

Chapter 5 Results and Discussion

5.1 Tensile Testing Results

5.1.1 As-Extruded Tubes

Figure 5.1 shows the tensile test results for the three samples in the as-extruded condition. The figure also shows the best fit Voce equation to the data.

Figure 5.1: Tensile testing data for three as-extruded samples fitted with equation.

The Voce equation has been shown to be the most applicable constitutive equation to model the strain hardening behavior of copper [22,26,28]. It was therefore applied to 49 the tensile test data in this research. The Voce equation’s material constants were determined with SciDavis data analysis software [33] as follows: A is 48,987 psi (338

MPa), B is 41,397 psi (285 MPa) while C is 5.5. Figure 5.1 depicts three tensile tests fitted with the Voce equation. The Voce equation provides a reasonably good fit to the data. Determination coefficients (R2 ) were calculated to be 0.996, 0.994 and 0.995, for

Tests 1, 2 and 3, respectively.

In an uniaxial tension test, the rate of work hardening is numerically equal to the stress level at instability [25].

̅ ̅ ̅ (40)

̅ is the effective (von Mises) true stress and ̅ is the true (effective) strain. This equation is used to calculate the instability strain (in uniaxial tension). Substituting the

Voce equation into this instability criterion, the instability strain can be predicted as a function of the material parameters for the constitutive equation.

̅ [ ] (41)

The instability strain ̅ was calculated to be 0.31 for the data presented in

Figure 5.1.

Figure 5.2 shows where ̅ ̅ for the experimental data and that calculated from the Voce equation intersect the stress-strain data.

50

Figure 5.2: Tensile instability strain in the as-extruded tubes predicted by

applying Voce equation.

As seen in Figure 5.2, the curve representing the Voce equation intersects with the curve representing its differentiation with respect to true strain. This intersection corresponds reasonably well to the instability strain (0.31) calculated earlier.

The ̅ ̅ determined from tensile test data (from Test 1) was also plotted in

Figure 5.2. Its intersection with the strain-stress curve shows a close correlation with the instability strain predicted. This curve follows the same trend as the differentiation of the 51

Voce equation. The instability strains from the three tensile tests were 0.296, 0.290 and

0.291. The average instability strain was 0.29, only 6.5% different than that predicted by the Voce equation.

5.1.2 Cold Rolled Tubes

Figure 5.3 shows the tensile test results for the two samples in the cold rolled condition. The cold rolled samples exhibited higher flow stress and less elongation to instability over the as-extruded samples. The quantitative difference will be discussed in section 5.1.4. Only two tests were performed for the material in this condition because the samples were produced in limited quantities.

Figure 5.3: Tensile testing data for 2 cold rolled samples fitted with

equation. 52

Figure 5.3 depicts two tensile test results fitted with Voce equation. A is 45,936 psi (317 MPa), B is 29,607 psi (204 MPa) while C is 5.8. Voce equation provides a good fit to the data. Determination coefficients (R2 ) were calculated as 0.963 and 0.973 for

Tests 4 and 6, respectively.

Substituting the material parameters into Equation 41, the instability strain was calculated to be 0.26.

Figure 5.4 shows where ̅ ̅ for the experimental data and that calculated from the Voce equation intersect the stress-strain data.

Figure 5.4: Tensile instability strain in the cold rolled tubes predicted by applying Voce equation. 53

As seen in Figure 5.4, the curve representing the Voce equation intersects with the curve representing its differentiation with respect to true strain. This intersection corresponds reasonably well to the instability strain (0.26) calculated earlier.

The ̅ ̅ curve developed from tensile test data (Test 6) is plotted in Figure

5.4. Its intersection with the strain-stress curve shows a close correlation with the instability strain predicted. This curve follows the same trend as the differentiation of the

Voce equation. The instability strains from two tensile tests were 0.251 and 0.254. The average instability strain was 0.25, only 4.0 % different than that predicted by the Voce equation.

5.1.3 Rolled and Heat Treated Tubes

Figure 5.5 shows the tensile test results for the two samples in the rolled and heat treated condition. The rolled-heat treated samples exhibited lower flow stress and higher elongation over the as-extruded samples and the cold rolled samples. The quantitative difference will be discussed in section 5.1.4.

54

Figure 5.5: Tensile testing data for two cold rolled, heat treated samples fitted with

equation.

Figure 5.5 also shows the best-fit Voce equation to the data. A is 49,307 psi

(340 MPa), B is 44,382 psi (306 MPa) while C is 5.2. Determination coefficients (R2) were calculated to be 0.999 and 0.999 for Tests 5 and 7, respectively. Substituting the material parameters into Equation 41, the instability strain was calculated to be 0.33.

Figure 5.6 shows where ̅ ̅ for the experimental data and that calculated from the Voce equation intersect the stress-strain data.

55

Figure 5.6: Tensile instability strain in the heat treated tubes predicted by applying Voce

equation.

As seen in Figure 5.6, the curve representing the Voce stress equation intersects with ̅ .̅ Its intersection with the Voce equation curve corresponds to the instability strain (0.33) calculated earlier.

The ̅ ̅ determined from tensile test data (from Test 5) was also plotted in

Figure 5.6. Its intersection with the strain-stress curve shows a close correlation with the instability strain predicted. This curve follows the same trend as the differentiation of the

Voce equation. The instability strains from the two tensile tests were 0.325and 0.320. 56

The average instability train was 0.32, only 3.1% different than that predicted by the

Voce equation.

It was shown that the Voce model provides a good fit to the tensile test data (R2

0.963) in each of the as-extruded, cold rolled and heat treated conditions. The Voce model also predicts the tensile instability strain reasonably accurately (within 6.5%). The

Voce material model meets the criteria of curve fit and the correlation of instability strain, thus it can be used as the basis of the predictive models to indicate the failure pressure of tubes.

5.1.4 The Effect of Cold Rolling and Heat Treatment Process on Uniaxial Tension Test

Figure 5.7 shows a comparison of tensile test data for tube in the as-extruded, the cold rolled, and the rolled and heat treated conditions. As somewhat expected, the cold rolled samples exhibited the highest flow stress and least elongation to instability, whereas the rolled and annealed samples exhibited the lowest flow stress but highest elongation. 57

Figure 5.7: Uniaxial strain-stress curves of samples in three different conditions.

Table 5.1 summarizes the results obtained from the data and appropriate calculations of the data shown in Figure 5.7. The cold rolled sample demonstrated a significant increase (~125%) in stress over the as-extruded sample. The cold rolling process caused a subsequent decrease in ductility. The decrease in the instability strain of the cold rolled sample was 14% when compared to the as-extruded sample. The rolled- heat treated samples showed a decrease in yield stress of ~45% over the as-extruded sample. The rolled-heat treated sample showed an increase in ductility over the as- 58 extruded sample; The instability strain of the rolled and heat treated sample increased by

10%.

Table 5.1: Comparison of results from uniaxial tensile testing

Yield Stress Average psi (MPa) Instability Strain

As-Extruded 8000 (55.2) 0.29 (Average of 3 tests) Cold Rolled 18010 (124.2) 0.25 (Average of 2 tests) Rolled-Heat Treated 4420 (30.5) 0.32 (Average of 2 tests)

5.2 Pressure Testing Results

5.2.1 As-Extruded Tubes

Figure 5.8 shows the pressure test results for the three samples in the as-extruded condition. 59

Figure 5.8: Pressure testing data for three as -extruded samples.

The pressure data are presented as a function of ram displacement, which is related to the volume displacement. Three samples in the as-extruded condition from tube no.1 were pressure tested to burst (Tests 8, 9, and 17). The failure of the tube corresponds to a sharp drop in pressure. Table 5.2 summarizes the burst pressures of the samples in the as-extruded condition. The maximum deviation between each value was less than 2%.

60

Table 5.2: Burst pressure results of the as-extruded tubes.

Test Failure Pressure psi (MPa) 8 5870 (40.5) 9 5860 (40.4) 17 5780 (39.9)

5.2.2 Cold Rolled Tubes

Figure 5.9 shows the pressure test results for the three samples in the cold rolled condition.

Figure 5.9: Pressure testing data for three cold rolled samples.

61

Three samples in the cold rolled condition from tube no.2 were burst tested (Tests

14, 15, and 16). Table 5.3 summarizes the burst pressures of the three tests. The maximum deviation between each value was less than 3%. The apparent discrepancy between the tests 14,15 and test 16 was attributed to some entrapped air during testing.

Table 5.3: Burst pressure results of the cold rolled tubes.

Test Burst Pressure psi (MPa) 14 5820 (40.1) 15 5730 (39.5) 16 5680 (39.1)

5.2.3 Rolled and Heat Treated Tubes

Figure 5.10 shows the pressure test results for the three samples in the rolled and heat treated condition, from tube no. 2. Table 5.4 summarizes the burst pressures of the three tests. Maximum pressures were all within 1% of each other. These values were also significantly less than those of the as-extruded and cold-rolled conditions. This is attributed to the metallurgical condition achieved for the simulated brazing cycle, and this will be discussed in section 5.3. 62

Figure 5.10: Pressure testing data for 3 rolled and heat treated samples.

Table 5.4: Burst pressure results of the rolled-heat treated tubes.

Test Burst Pressure psi (MPa) 11 5160 (35.5) 12 5180 (35.7) 13 5190 (35.8)

5.2.4 The Effect of Cold Rolling and Heat Treatment Process on the Pressure Test

Availability of tube for testing and the tube lengths from a single extrusion trial were limited. Tube no.1 was the only tube for which all conditions, as-extruded, cold rolled, and rolled-heat treated, were pressure tested. Thus, these pressure test results 63 provide a reasonable assessment of the effect of the cold rolling and heat treatment process on failure pressure (negating variability that may be incurred from separate extrusion trials). Figure 5.11 compares the test pressure-ram displacement curves of an as-extruded sample, a cold rolled sample and a rolled-heat treated sample from tube no.1.

As expected, and consistent with previous work with aluminum tube [7,14], the cold- rolled sample exhibited the highest burst pressure and the cold rolled and heat-treated sample failed at the lowest pressure.

64

Figure 5.11: Comparison of test pressure-ram displacement of an as-extruded sample, a

cold rolled sample, and a rolled-heat treated sample.

Table 5.5 summarizes the burst pressure results obtained from the data shown in

Figure 5.11. Only one pressure test was performed on each of the cold rolled and rolled- heat treated samples. For the as-extruded samples, three pressure tests were performed and an average was taken of the measured burst pressures. As seen in Figure 5.11, the cold rolled sample demonstrated an increase in burst pressure over the as-extruded sample. This was calculated to be about a 6% change. The increase in burst pressure of 65 the cold rolled sample is due to the strain hardening in the internal walls and an increase in the thickness of the walls. The rolled-heat treated sample showed a 7% decrease in burst pressure over the as-extruded sample. The decrease in burst pressure of the rolled- heat treated sample is related to metallurgical changes such as grain coarsening and possibly recovery during the brazing cycle.

Table 5.5: Burst pressure results of an as-extruded sample, a cold rolled sample, and a

rolled-heat treated sample.

Sample Burst Pressure psi (MPa) As-Extruded 5860 (40.4) Cold Rolled 6180 (42.6) Rolled and 5450 (37.6) Heat Treated

5.2.5 Tube Failure

Three different types of tube failure were observed in pressure tested samples.

Figure 5.12 shows the external feature of the first type of tube failure.

66

Figure 5.12: External feature of the first type of tube failure

As can be seen in Figure 5.12, bulging occurred across approximately three- fourths of the tube. In the bulging region, the internal walls failed during the test. The outer wall failed after that of the internal walls.

Figure 5.13 shows the external feature of the second type of tube failure. 67

Figure 5.13: External feature of the second type of tube failure

As seen in Figure 5.13, bulging occurred across the entire tube. All of the internal walls failed during the test. The outer wall failed after that of the internal walls.

Figure 5.14 shows the external feature of the third type of failed sample 68

Figure 5.14: External feature of the third type of tube failure

As seen in Figure 5.14, all of the internal walls failed during the test. The outer walls at both ends failed instantaneously after that of the internal walls.

As seen from Figures 5.12-5.14, initial failure occurs at the internal walls before fully bursting. It is evident that the maximum stress occurs in the internal walls (up until their failure). This result validates the assumption made earlier in developing the analytical model.

5.3 Microstructure Results

Figure 5.15, 5.16 and 5.17 demonstrate the microstructure of UNS 122000 copper samples that are in the as-extruded, cold rolled, rolled-heat treated conditions. Figure

5.15 demonstrates the grain structure of the as-extruded sample before the simulated 69 brazing cycle. Figure 5.17 demonstrates the grain structure of the rolled-heat treated sample after the simulated brazing cycle. Metallography of the rolled-heat treated sample indicates that recrystallization did not occur during the simulated brazing cycle, in contrast to what is typical with aluminum tube. As shown in Figure 5.17, modest grain coarsening was found from the rolled-heat treated sample after the brazing cycle.

Recovery is also implied. The associated metallurgical changes result in a change in mechanical properties such as strength. The grain size in the internal wall before and after the brazing cycle was determined with the line intercept method. The as-extruded sample possessed an average grain size of 46 . The rolled-heat treated sample possessed a grain size of 87 . The yield strength of the material with different grain size can be calculated by the Hall-Petch relation [25]. The Hall-Petch relation is given in

Equation 42.

(42)

and are the material constants. is 20 MPa (2900 psi) for the copper. is 0.14 MPa (20 psi ) for the copper [34]. Substituting the grain size of the as- extruded samples and the rolled-heat treated samples into Equation 42, the yield strength of the cold rolled samples and rolled-heat treated samples can be calculated. The decrease in the yield strength after the simulated brazing cycle was calculated to be around 14%. But this does not entirely account for the difference that is presented in

Figure 5.7. The decrease in failure pressure of the rolled-heat treated sample can be attributed to these metallurgical changes such as grain coarsening and possibly recovery during the brazing cycle. 70

Figure 5.15: UNS 122000 copper multi-channel tube in as-extruded condition.

Figure 5.16: UNS 122000 copper multi-channel tube in cold rolled condition.

71

Figure 5.17: UNS 122000 copper multi-channel tube in rolled-heat treated condition.

5.4 Burst Models

Two predictive models were used to predict the failure pressure of the tube during a burst test. The first predictive model was developed by Kraft and Miller [18]. Another new predictive model was developed in this research.

5.4.1 Miller and Kraft Model

The Kraft and Miller predictive model [18] can be used to predict the failure pressure of the tube. The Kraft and Miller predictive model (Equation 33) predicts failure pressure as a function of the instability strain, initial dimensions, and effective stress. 72

Substituting the Voce equation determined earlier into the instability criterion

(Equation 32), the tube instability strain can be calculated. The results are presented in

Table 5.6.

Table 5.6: Instability strains of pressurized samples predicted by Kraft and Miller model.

As-Extruded Sample Cold Rolled Sample Rolled-Heat Treated sample Instability Strain 0.23 0.18 0.25

Substituting the instability strain into the Voce equation, the effective stress can be calculated. The initial dimensions of the tube are presented in Appendix Table A1-

A6. Using these data, the failure pressure was predicted by applying Equation 33. Table

5.7 shows the comparison of the measured and the predicted failure pressures.

Table 5.7: Pressure test results and Kraft-Miller model predictions

Sample Measured Failure Predicted Failure % Difference Pressures Pressures psi (MPa) psi (MPa) As- Tube 5840 (40.3) 5850 (40.3) -0.2% Extruded no.1 (Average of 3 tests) Cold Tube 6180 (42.6) 6060 (41.8) 1.9% Rolled no.1 Tube 5740 (39.6) 5670 (39.1) 1.2% no.2 (Average of 3 tests) Rolled and Tube 5450 (37.6) 5660 (39.0) -3.9% Heat no.1 Treated Tube 5170 (35.6) 5340 (36.8) -3.3% no.2 (Average of 3 tests)

Only one pressure test was performed on each of the cold rolled and rolled-heat treated samples from tube no.1; These measured failure pressures were compared to the 73 predicted failure pressures, as shown in Table 5.7. For each of the other tubes and conditions shown in Table 5.7, three tests were performed and an average was taken of the measured failure pressures to compare with the predicted failure pressures. It is noted, that the measured failure pressures from each tube in the same condition have a small discrepancy, the maximum is calculated to be 7.7%. This discrepancy could be attributed to the difference of the initial dimensions between the two tubes. These two tubes were extruded with the same process, however, some variation of process conditions can lead to dimensional and metallurgical variation that effect mechanical behavior.

As seen in Table 5.7, the Kraft and Miller predictive model indicated failure pressure to within 4% of the measured data. The predictive model overestimated the failure pressure for the as-extruded sample by about 1%. The predicted failure pressure of the cold rolled sample was within 2% of the measured pressure. The predictive model overestimated the failure pressure for the rolled-heat treated sample by 4%.

5.4.2 New Model

The predictive model developed in this research will be compared to the predictive model of Kraft and Miller [18]. The new predictive model (Equation 29) predicts failure pressure as a function of the instability strain, initial dimensions of the tube, material constants of the constitutive equation, and dimension factor (dimension factor is the ratio between the channel width and the internal wall thickness during deformation). 74

Substituting the initial dimensions (ratio between and ), the dimension factor, and the Voce equation determined earlier into the instability criterion (Equation

34), the tube instability strain can be calculated numerically. As seen in Table 5.8, the results are compared to the instability strain predicted by Kraft and Miller’s instability criterion.

Table 5.8: Instability strains of pressurized samples predicted by new model.

As-Extruded Sample Cold Rolled Sample Rolled-Heat Treated Sample Ratio ( / ) 0.233 0.237 0.219 0.234 0.219 Instability 0.230 0.180 0.180 0.250 0.250 Strain (Kraft) Instability 0.246 0.188 0.192 0.266 0.269 Strain (New) % Difference 7.0% 4.4% 6.7% 6.4% 7.6%

As seen in Table 5.8, the instability strain predicted by the new model is dependent on the ratio of the wall thickness to the channel width ( / ). In contrast, the instability strain predicted by Kraft and Miller’s model is not dependent on the ( /

) ratio. The instability strains predicted by two instability criterions were within 8%.

Knowing the instability strain, the failure pressures were predicted by applying

Equation 34. Only one pressure test was performed on each of the cold rolled and rolled- heat treated samples from tube no.1. For each of the other tubes and conditions shown in

Table 5.9, three tests were performed and an average was taken of the measured failure pressures to compare with the predicted failure pressures.

75

Table 5.9: Pressure test results and new model predictions

Sample Measured Failure Predicted Failure % Pressures Pressures Difference psi (MPa) psi (MPa) As- Tube no.1 5840 (40.3) 5900 (40.7) -1.0% Extruded (Average of 3 tests) Cold Tube no.1 6180 (42.6) 6070 (41.9) 1.8% Rolled Tube no.2 5740 (39.6) 5730 (39.5) 0.2% (Average of 3 tests) Rolled and Tube no.1 5450 (37.6) 5740 (39.6) -5.3% Heat Tube no.2 5170 (35.6) 5480 (37.8) -6.0% Treated (Average of 3 tests)

From Table 5.9, the new predictive model indicated failure pressure to within 6% of the measured data. The predictive model overestimated the failure pressure for the as- extruded sample by about 1%. The predicted failure pressure of the cold rolled sample was within 2% of the measured pressure. The predictive model overestimated the failure pressure for the rolled-heat treated sample by 6%.

The overestimation for the rolled-heat treated failure pressure can be attributed to the inherent inhomogeneity in the tube due to processing. This inhomogeneity is obvious in Figures 1.4 and 1.5, where the internal wall of the AA 3102 alloy recrystallized and experienced severe grain growth during the simulated brazing. The cold work induced during the cold rolling process is the driving force for recrystallization and grain growth during the simulated brazing cycle [17]. The stored energy from the cold rolling is released during the simulated brazing cycle. This stored energy causes the internal walls to recrystallize and experience grain growth [32]. The grain growth reduces the strength of the internal walls because the grain boundary strengthening is decreased. Kraft and

Williams [14] showed that the grain growth after the simulated brazing cycle caused a 76

22% reduction in failure pressure of AA 3102 aluminum tube when the tube thickness had a 3% thickness reduction. In contrast, the metallography of the UNS 122000 copper samples only illustrates grain coarsening after the simulated brazing (recovery is implied). The metallography indicates that recrystallization did not occur but that grain growth or coarsening was experienced. A possible explanation is that the cold rolling

(5% thickness reduction) did not provide enough cold work for the copper to recrystallization whereby severe grain growth could occur during the simulated brazing cycle. The rolled-heat treated sample demonstrated a 7% decrease in failure pressure after the simulated brazing cycle.

The Kraft and Miller predictive model and the new predictive model overestimated the failure pressures for the rolled-heat treated samples by 4% and 6%, respectively. These discrepancies can be attributed to material inhomogeneity. The material constants of the Voce equation were determined from an entire sample during the uniaxial tensile test. Since most of the grain coarsening is located at the internal walls after the simulated brazing cycle, the strength of the internal wall would be weaker than the model predicts.

Kraft and Miller’s instability criterion is expressed as ̅ ̅ √ ̅. Instability strains predicted by Kraft and Miller’s criterion are only dependent on the material constants of the Voce equation. This instability strains predicted by Kraft and Miller criterion are not dependent on the ( / ) ratio (which accounts for variations in 1 and

3). In contrast, the instability strains predicted by the new criterion (Equation 34) are dependent on the ( / ) ratio. The samples in the same condition with different ( / 77

) ratio will yield different instability strains. This difference is very small (less than

2.2% in this research).

The new predictive model developed in this research was used to analyze tubes with rectangular channels. This new predictive model provided accurate predictions of the failure pressures (discrepancy 6% ). The Kraft and Miller’s predictive model was originally developed to predict the failure pressures of tubes with circular channels. The

Kraft and Miller predictive model’s ability to predict the failure pressures of tubes with rectangular channels was also accurate (discrepancy 4%). In comparison, the Kraft and

Miller’s predictive model is slightly more accurate than the new model.

78

Chapter 6 Conclusions

6.1 Summary and Conclusions

In this research, an analytical model was developed to predict the mechanical response and failure pressure of copper multi-channel tube for HVACR systems. This model predicts failure pressure as a function of the instability strain, initial dimensions of the multi-channel tube and material constants determined from tensile testing. During pressure testing, failure occurs at the internal walls and this coincides with the maximum pressure. The instability strain of the pressurized tube is also predicted with this model.

Samples in the as-extruded, cold rolled, and rolled-heat treated conditions were tested in uniaxial tension. Tensile testing of the tube samples was used to determine the materials’ stress-strain relationships (constitutive equations). The Voce equation was selected to be the constitutive equation to model the strain-stress relationship of the samples. The Voce equation correlated well to the tensile test data (R2 0.963) in the as- extruded, cold rolled and heat treated conditions. The Voce model also predicted the tensile instability strain accurately (within 6.5%). Thus it can be used as the basis of the predictive models to predict the failure pressure of UNS122000 copper tubes.

This analytical model was validated by pressure tests using samples in the as- extruded, cold rolled, and rolled-heat treated conditions. The analytical model predicted failure pressures to within 6% when compared to measured values. The predicted failure pressure of the as-extruded sample was within 1.0% of the measured failure pressure. 79

The cold rolled and rolled-heat treated samples had discrepancies of 1.8% and 6.0% when compared to measured values.

The cold work induced during the rolling process affects the mechanical properties of tubes. The cold rolled sample demonstrated a 125% increase in yield stress over the as-extruded sample. The decrease in uniaxial instability strain of the cold rolled sample was 14% when compared to the as-extruded sample. The cold rolled sample demonstrated a 6% increase in failure pressure over the as-extruded sample.

The simulated brazing process affected the mechanical properties of tubes. The samples underwent grain coarsening during the simulated brazing process. The rolled- heat treated sample demonstrated a 45% decrease in yield strength compared to the as- extruded sample. The increase in uniaxial instability strain of the rolled-heat treated sample was 10% compared to the as-extruded sample. The rolled-heat treated sample demonstrated a 7% decrease in failure pressure over the as-extruded sample. The analytical model derived in this research was compared to the Kraft and Miller’s predictive model. The predicted tube instability strain was within 8% of the predicted instability strain based on Kraft and Miller’s model. The Kraft and Miller model predicted failure pressure to within 4% of the measured failure pressure, which is slightly more accurate than the new model.

Even though the Kraft and Miller’s predictive model was used to analyze tubes with circular channels, it may be used to predict the failure pressure of tubes with rectangular channels (discrepancy 4%). 80

6.2 Future Work

The tensile and pressure tests in this research were conducted at room temperature. This new analytical model was only feasible to predict the failure pressure of the tubes at room temperature. To further analyze the influence of temperature on the mechanical properties of the UNS 122000 copper multi-channel tube, the tensile test and pressure tests should be conducted at several elevated .

The prediction of the failure pressure and the instability strain of a pressurized tube were related to the initial dimensions of the cross-section. To validate the model’s ability to predict the failure pressure consistently, the tensile and pressure tests should be conducted with tubes of other initial dimensions.

81

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85

Appendix: Initial Dimensions of the Cross-Section

Figure A1: Tube Profile

86

Table A1: Initial dimension of as-extruded sample from tube No.1.

Channel Wall Measurement t/W width Thickness (mm) ratio 1 1.226 a 0.274 0.237 2 1.104 b 0.307 0.279 3 1.100 c 0.307 0.280 4 1.087 d 0.321 0.295 5 1.092 e 0.319 0.292 6 1.090 f 0.322 0.298 7 1.071 g 0.323 0.297 8 1.100 h 0.311 0.282 9 1.096 i 0.300 0.273 10 1.105 j 0.270 0.233 11 1.216

87

Table A2: Initial dimension of cold-rolled sample from tube No.1.

Channel Wall Measurement t/W width Thickness (mm) ratio 1 1.245 a 0.275 0.237 2 1.075 b 0.332 0.309 3 1.071 c 0.326 0.302 4 1.086 d 0.326 0.302 5 1.073 e 0.328 0.304 6 1.081 f 0.325 0.301 7 1.078 g 0.328 0.303 8 1.088 h 0.326 0.299 9 1.088 i 0.318 0.294 10 1.078 j 0.277 0.239 11 1.242

88

Table A3: Initial dimension of heat treated sample from tube No.1.

Channel Wall Measurement t/W width Thickness (mm) ratio 1 1.236 a 0.273 0.236 2 1.072 b 0.324 0.302 3 1.075 c 0.335 0.312 4 1.075 d 0.338 0.314 5 1.076 e 0.336 0.312 6 1.076 f 0.329 0.306 7 1.070 g 0.336 0.313 8 1.075 h 0.330 0.306 9 1.082 i 0.328 0.303 10 1.080 j 0.273 0.234 11 1.247

89

Table A4: Initial dimension of as-extruded sample from tube No.2.

Channel Wall Measurement t/W width Thickness (mm) ratio 1 1.178 a 0.251 0.217 2 1.091 b 0.304 0.280 3 1.079 c 0.331 0.305 4 1.088 d 0.323 0.297 5 1.084 e 0.322 0.298 6 1.077 f 0.326 0.300 7 1.093 g 0.317 0.289 8 1.096 h 0.307 0.279 9 1.101 i 0.317 0.288 10 1.096 j 0.245 0.212 11 1.219

90

Table A5: Initial dimension of cold-rolled sample from tube No.2.

Channel Wall Measurement t/W width Thickness (mm) ratio 1 1.245 a 0.254 0.219 2 1.081 b 0.320 0.297 3 1.075 c 0.337 0.314 4 1.071 d 0.339 0.317 5 1.066 e 0.339 0.316 6 1.079 f 0.340 0.315 7 1.077 g 0.339 0.315 8 1.073 h 0.338 0.315 9 1.072 i 0.337 0.315 10 1.066 j 0.275 0.242 11 1.205

91

Table A6: Initial dimension of as-extruded sample from tube No.3.

Channel Wall Measurement t/W width Thickness (mm) ratio 1 1.237 a 0.256 0.216 2 1.128 b 0.311 0.279 3 1.101 c 0.312 0.283 4 1.101 d 0.318 0.288 5 1.100 e 0.316 0.287 6 1.095 f 0.323 0.294 7 1.098 g 0.318 0.289 8 1.096 h 0.318 0.290 9 1.095 i 0.304 0.278 10 1.092 j 0.276 0.242 11 1.188

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