Instability and Failure in Aluminum Multi-Channel Tubing
INSTABILITY AND FAILURE IN ALUMINUM MULTI-CHANNEL TUBING
A thesis presented to
the faculty of
the Fritz J. And Dolores H. Russ College of Engineering and Technology
of Ohio University
In partial fulfillment
of the requirements for the degree
Master of Science
Harvey (Beau) S. Miller
March 2006
This Thesis entitled
INSTABILITY AND FAILURE IN ALUMINUM MULTI-CHANNEL TUBING
by
HARVEY (BEAU) S. MILLER
has been approved for
the Department of Mechanical Engineering
and the Russ College of Engineering and Technology by
Frank F. Kraft
Assistant Professor of Mechanical Engineering
Dennis Irwin
Dean, Russ College of Engineering and Technology
MILLER, HARVEY (BEAU) S., M.S. March 2006. Mechanical Engineering
Instability and Failure in Aluminum Multi-Channel Tubing (75 pp.)
Director of Thesis: Frank F. Kraft
The purpose of this research was to examine the mechanical and structural
behavior of aluminum micro-channel tube used in CO2 based automotive parallel flow
heat exchangers. An analytical model was developed and extended to predict failure
pressure of the tubing at normal operating conditions (20 to 180o C). The model
developed in this study is based upon the instability strain of structural members in a
plane-strain stress state. An experimental test apparatus was upgraded and integrated
with computer software for trouble-free burst test operation. Room temperature burst
tests were conducted on micro-channel tube samples in alloys 1197, AA 3003 and
AA3102 to validate the accuracy and universality of the model to within 6% of actual
measured values. Constitutive equations were also developed, by means of standard
uniaxial tensile testing to provide material data for the model. The model was extended
to predict failure pressures at elevated temperatures to within 8% of experimental test
values. The data are being used to assist designers in developing and optimizing CO2 based climate control systems in automobiles.
Approved:
Frank F. Kraft
Assistant Professor of Mechanical Engineering
Acknowledgements
First and foremost I would like to thank Dr. Frank F. Kraft. Without his guidance and perseverance this work could not have been completed in a timely fashion. I would also like to thank Dr. Sang-Soo Kim and Dr. Bhavin Mehta for their encouragement and being members on this thesis committee. Special thanks to Gowreesan Vamadevan for conducting the metallography on my test specimens.
The author would also like to thank Brazeway, Inc. of Adrian, Michigan and
Erbsloeh Aluminum GmBH of Velbert, Germany for their financial support. These industrial sponsors also provided all test samples and conducted all chemical analyses.
v
Table of Contents
CHAPTER 1 ...... 1
INTRODUCTION ...... 1
1.1 Background...... 1
1.2 Operating Conditions of R744...... 2
1.3 Environmental Advantages of CO2...... 4
1.4 Parallel Flow Heat Exchanger ...... 4
1.5 Historical Review...... 5
1.6 Objectives ...... 7
1.7 Test Apparatus ...... 9
CHAPTER 2 ...... 10
ANALYTICAL MODEL...... 10
2.1 Analysis Assumptions...... 10
2.2 Künesh Method...... 10
2.3 Instability Analysis ...... 12
2.4 Validating State of Stress...... 17
CHAPTER 3 ...... 20
MATERIAL...... 20
3.1 Alloys...... 20
3.2 Tube Geometry ...... 20
3.3 Sample Profile...... 21
3.4 Manufacturing and Handling Processes...... 22 vi
3.4.1 Hot Extrusion of Micro-Channel Tube...... 22
3.4.2 Material Handling and Roll Sizing ...... 22
CHAPTER 4 ...... 24
EXPERIMENTAL PROCEDURE ...... 24
4.1 Simulated Brazing Cycle ...... 24
4.2 Effects of Brazing ...... 25
4.3 Tube Furnace ...... 29
4.4 Simulated Thermal Procedure...... 32
4.5 Development of Constitutive Equations ...... 32
4.6 Tensile Testing...... 34
4.7 Room Temperature Static Burst Testing...... 37
4.7.1 Test Apparatus ...... 38
4.7.2 Room Temperature Experimental Set-up ...... 39
4.7.3 MTS Room Temperature Test Procedure...... 41
4.8 Improving Elevated Temperature Burst Testing...... 42
4.8.1 Upgrading Convection Heater ...... 42
4.8.2 Improving Temperature Control...... 43
4.9 Elevated Temperature Burst Testing...... 44
4.9.1 MTS Elevated Temperature Test Procedure...... 44
CHAPTER 5 ...... 47
RESULTS AND DISCUSSION...... 47
5.1 Tensile Testing Results...... 47 vii
5.1.1 Alloy 1197 Constitutive Equation ...... 48
5.1.2 AA 3003 Constitutive Equation...... 49
5.1.3 AA 3102 Constitutive Equation...... 50
5.2 Uncertainty Analysis...... 51
5.3 Tube Failure...... 52
5.4 Room Temperature Analysis ...... 53
5.5 Statistical Analysis...... 55
5.6 Elevated Temperature Testing Analysis ...... 56
CHAPTER 6 ...... 59
CONCLUSIONS...... 59
6.1 Conclusions...... 59
6.2 Future Work...... 61
REFERENCES: ...... 63
viii
List of Tables
Table Page
3-1: Chemical composition of alloys used during experimentation (determined with optical emission spectroscopy) ...... 20
3-2: Initial channel diameter and web thickness, measured from tubes of each of the 3 alloys...... 21
4-1: Initial measurement of tensile specimens...... 32
4-2: Final dimensions of the deformed samples ...... 37
5-1: Measured (actual) burst pressures, of the three alloys, at room temperature...... 55
5-2: Predicted burst pressures at room temperature and percent differences from the actual, measured values ...... 55
5-3: Reduction values per C, determined from data presented in Figure 5-6...... 57 v
List of Figures
Figure Page
1-1: Pressure-enthalpy diagram for an R744 based climate control system. Numbered points on the diagram correspond to those in Figure 1-2 [4]...... 3
1-2: System components for R744 climate control system [4]...... 4
1-3: Standard automotive heat exchanger [6] ...... 5
1-4: Test apparatus, MTS machine and computer ...... 9
2-1: Superpositioning of two tangential stress distributions onto channels of micro- channel tube. a is internal radius, b is external radius, Pi is internal pressure, Po is
external pressure and σt is the tangential stress across the wall...... 11
2-2: Idealized pressure versus strain curve. Initial, non-linear portion of curve is due to test apparatus compliance...... 13
2-3: Results of a finite element analysis on the internal wall of the micro-channel tube.
The stress ranges from 68.0MPa in the center to 97.2MPa at the surface [10] ...... 17
2-4: Stress distribution in the wall of the micro-channel shown in Figure 2-3 using finite
element analysis (FEA) and Equations 1, 4 and 16 [11]...... 18
3-1: Sketch of experimental R744 tube profile used during experimentation...... 21
4-1: Standard automotive parallel flow heat exchanger [6]...... 24
4-2: 1197 in pre-braze condition...... 26
4-3: 1197 in post-braze condition ...... 27
4-4: 3102 in pre-braze condition...... 27
4-5: 3102 in post-braze condition ...... 28 vi
4-6: 3003 in pre-braze condition ...... 28
4-7: 3003 in post-braze condition ...... 29
4-8: Thermolyne tube furnace and Love controller used for simulated brazing cycle .....30
4-9: Tube holder with two samples, and equipped with three thermocouples on a dummy sample ...... 31
4-10: Thermocouple temperatures displayed to computer monitor...... 31
4-11: Tensile test apparatus with extensometer...... 34
4-12: Data acquisition’s home screen, reflecting a compressive force...... 35
4-13: Visible “tree bark” like grain structure of the post-tested tubes...... 36
4-14: Computer controlled MTS machine and burst testing station...... 38
4-15: MTS machine and components of the burst testing station...... 39
4-16: Selected components of burst test apparatus...... 40
4-17: Room temperature burst testing procedure...... 41
4-18: Omega forced-air convective resistance heater...... 43
4-19: Elevated temperature burst testing procedure ...... 45
5-1: 1197 tensile testing data for 3 samples fitted with a 2nd order exponential function.
Empirical exponential function was numerically determined with Origin plotting software...... 47
5-2: AA 3003 tensile testing data for 3 samples fitted with power law hardening model
...... 49 vii
5-3: AA 3102 tensile testing data for 3 samples fitted with a 2nd order exponential function. Empirical exponential function was numerically determined with Origin plotting software ...... 51
5-4: Cross-sectional view of multi-channel tubing before and after failure ...... 52
5-5: Typical test pressure versus ram displacement curve...... 54
5-6: Burst pressure as a function of temperature for all 3 alloys...... 56
5-7: Actual elevated temperature failure pressures and predicted values, using Equation
5.3, for each of the 3 alloys...... 58
1
CHAPTER 1
INTRODUCTION
As the internal combustion engine becomes more efficient combined with the
onset of hybrid vehicle technology, conventional refrigerants (i.e., R134a) become less effective for climate control purposes. However, replacing refrigerant R134a with CO2
(designated R744) requires an increase in mechanical properties in climate control system
components. This research presents a predictive (analytical) model to assist designers in
the design of micro-channel tubing used in automotive parallel flow heat exchangers.
This model is validated by a series of static burst tests, using an improved method of experimentation.
Chapter 1 presents a brief background of research significance and prior work, the
objectives of the work, work that was completed and a basic overview of the test
apparatus used.
1.1 Background
The primary goal of this research is to assist designers in improving climate
control systems in automobiles. Currently, Ethylene Glycol (and excess engine heat) and
Fluorocarbon refrigerant 134a (R134a) are the working fluids used in the heating and
cooling processes, respectively. But as the internal combustion engine becomes more
efficient and hybrid vehicles become more prominent, the cogeneration possibilities
diminish. So the push for an increase in efficiency has prompted designers to develop a system that incorporates both processes using the same working fluid, CO2 (refrigerant 2
R744). However, CO2 systems operate at a much higher pressure and temperature (15.8
MPa and 180 oC) than R134a (4.1 MPa and 120 oC), which is one of the major contributing factors to this research [1].
In 1987 international negotiators adopted the Montreal Protocol to protect the
earth’s ozone layer from being depleted. As of 2002, 183 countries have ratified this
protocol to reduce the consumption of ozone depleting substances (ODS) [2]. More
recently, the Kyoto Protocol (1997) has been sanctioned to extend focus beyond ozone
depletion, to include global warming [3]. This push for more environmentally friendly
substances scrutinizes conventional refrigerants such as R134A and envisions R744 as a
safe refrigerant for the future.
1.2 Operating Conditions of R744
Due to the severity of R744’s operating conditions compared to that of R134a,
system component requirements increase. These component design requirements are
based on the CO2 system’s operating conditions throughout the refrigeration cycle.
Figure 1-1 depicts a pressure versus enthalpy diagram of the aforementioned cycle. The
numbered points in Figure 1-1 correspond to the system components in Figure 1-2. 3
Figure 1-1: Pressure-enthalpy diagram for an R744 based climate control system. Numbered points on the diagram correspond to those in Figure 1-2 [4].
1-2 adiabatic compression stage (3.5 to 13 MPa and 30 to 160 C) 2-3 constant pressure cooling, gas cooler (160 to 45 C @ 13 MPa) 3-4 additional cooling via internal heat exchanger (45 to 35 C @ 13 MPa) 4-5 adiabatic expansion (13 to 3.5 MPa and 45 to 0 C) 5-6 constant pressure and temperature evaporation (0 C @ 3.5 MPa) 6-1 adiabatic heating via internal heat exchanger (0 to 30 C, @ 3.5 MPa)
4
Figure 1-2: System components for R744 climate control system [4].
1.3 Environmental Advantages of CO2
CO2 has been proven to have a less detrimental effect on the environment as compared to R134a. Global Warming Potentials (GWPs) are a quantitative measure of a specific green house gas’s effect on global warming when compared to a reference gas.
R134a has a GWP 1300 times greater than that of CO2 [5]. Hence CO2 surpasses R134a when examined environmentally.
1.4 Parallel Flow Heat Exchanger
The main focus of this study is concerned with the mechanical behavior and structural design of the multi-channel tubing used in heat exchangers within the automotive climate control system. The heat exchanger is comprised of a parallel array 5 of brazed, multi-channel tubes and fins connected between two header tanks (see Figure
1-3).
Figure 1-3: Standard automotive heat exchanger [6].
In the CO2 refrigeration cycle, the heat exchanger acts as a gas cooler (versus a
condenser) since the CO2 is supercritical and a phase change is not present. The gas
cooler supercools (removes heat) from the compressed CO2 flowing through the internal
channels. The presence of this high-pressure condition prompts the need for material
properties for typical alloys used in the production of these heat exchangers.
1.5 Historical Review
CO2 based climate control systems have not yet been implemented into today’s
automobiles; therefore, documentation pertaining to the aluminum micro-channel tubing, 6 specific to these parallel flow heat exchangers is not widely published. However, the tubing used in R134a climate control systems has been examined.
Guzowski, et al. [7] investigated process-structure-property relationships for typical aluminum alloy used during fabrication of parallel flow heat exchangers. It was shown that the critical amount of strain, imposed on micro-channel tubing, occurs at 4 to
7% thickness reduction. This critical amount of strain is the driving force for very large grains during the thermal processing. These larger grains produce reduced burst pressures, in rectangular micro-channel tubing.
Kraft, et al. [8] examined the mechanical response, due to internal pressurization, of aluminum micro-channel tube for three different profiles. A model was proposed to predict burst pressure and material response at failure, as a function of material parameters, initial and final tube geometry. Hydrostatic pressure data were used in determining the effective stress in the internal walls at failure. The true stress and strain data was then established.
Künesch [9] derived a formula for the stress at the web center (internal walls) of circular channel tubing. He analyzed the tubing as a series of individual parallel channels. In doing this, adjacent channels could be superimposed upon one another. The internal pressure acting at the web center of two adjacent channels was then used to develop a formula for the effective stress at this critical location.
Vamadevan [10] validated the state of stress experienced at the web center of a circular channel tube. He performed a finite element analysis (FEA), using MSC Marc software, to develop the stress distribution for an internally pressurized tube. The results 7 were then compared to the analytical model and a graphical comparison was presented.
Differences between the mean stresses of both methods were the driving force for the analysis. Vamadevan’s work also illustrated a decrease in material properties due to the change in microstructure during brazing.
1.6 Objectives
The main objectives of this research are the development and validation of a predictive model, and improving the testing equipment to accomplish the goals of the validation. Listed below are the main objectives, as well as brief descriptions, and any secondary objective required to complete the main objective.
• Develop a mathematical model to assess the failure pressure of multi-channel
tube for gas coolers.
o Model will yield instability strain, dimensions, effective stress, and
maximum pressure
o Model will predict burst pressure/failure of a tube as a function of
material properties and dimensions
o Assumptions made for model development
Circular tube channels
Plane strain stress state
Failure occurs at internal walls
Isotropy/homogeneity
8
• Improve testing capabilities
o Upgrade heater and temperature controller for elevated temperature
pressure tests
Integrate temperature controller with computer controlled MTS
machine for trouble free operation
Replace old heater with higher powered forced convection
heater
• Validate model
o Simulate thermal (brazing) cycle on tube samples
o Develop constitutive equations from tensile tests
o Conduct pressure tests on tube samples
o Examine and measure tube geometry at failure/instability
• Evaluate different alloys (further validating model)
o Repeat simulated brazing cycle, development of constitutive
equations, maximum pressure tests and measurements of failed
samples
o Selected alloys are 1197, AA3003 and AA3102
• Quantify reduction in burst properties as a function of temperature
o Determine relationship between burst pressure and temperature
9
1.7 Test Apparatus
The apparatus used for this research consists of a hydraulic cylinder, fittings, controls and quick disconnects capable of withstanding 69 MPa (10,000 psi) of pressure
(Figure 1-4).
MTS Machine
Testing Station
Figure 1-4: Test apparatus, MTS machine and computer.
When integrated with the MTS machine, the MTS software can control the hydraulic
cylinder’s pressure, displacement, and force in order to develop pressure within a tube
sample. The test apparatus is fully described in section 4.7.1. 10
CHAPTER 2
ANALYTICAL MODEL
2.1 Analysis Assumptions
To begin this analysis a few assumptions were made:
• Circular channel tube design
• Plane strain stress state
• von Mises (effective) stress and strain
• Failure occurs at instability
• Failure occurs at interior wall (web) center
• Superimpose tangential and radial stress derived from cylinder analysis (Figure 2-1)
• Neglect elastic deformation
2.2 Künesh Method
During normal operation of a parallel flow heat exchanger, the micro-channel tubing is subjected to internal pressure. Due to the geometric configuration of the tube, the maximum stress achieved occurs at the web center of two adjacent channels. Künesh proposed that by superimposing the internal pressures acting at the center of the web onto the middle of two adjacent channels, a formula for effective stress could be developed
[9]. Figure 2-1 depicts two adjacent channels superimposed onto one another.
11
Po=0
σt
Figure 2-1: Superpositioning of two tangential stress distributions onto channels of micro-channel tube. a is internal radius, b is external radius, Pi is internal pressure, Po is external pressure and σt is the tangential stress across the wall.
From Shigley and Mitchell [11] the tangential stress (σt) of an internally
pressurized cylinder is given by:
2 2 Pa i ⎡ b ⎤ σ t = 22 ⎢1+ 2 ⎥ (2.1) − ab ⎣ r ⎦
where r is the distance from the center of the cylinder.
By integrating the tangential stress, resulting from superimposing two cylinders onto one
another (Equation 2.2), the average tangential stress (σ tave ) across the web thickness is given by:
2 b σσ == σ dr (2.2) 1 tave ∫ t − ab a 12
D Let: a = and − = tab (2.3) 2
Substituting Equation 2.3 and 2.1 into 2.2 simplifies to Equation 2.4.
DP σ = i (2.4) 1 t
Where D is the channel diameter and t is the web thickness (at the center of the wall). From inspection, the internal pressure creates a radial stress of:
σ 3 = −Pi (2.5)
Since a plane strain stress state is assumed the σ 2 principal stress becomes the
hydrostatic stress component which is equivalent to the average of σ 1 and σ 3 [8].
Solving Equation 2.4 for Pi :
σ t P = 1 (2.6) i 2r
Equation 2.6 expresses internal pressure in terms of channel radius r, web thickness t and
the principle stress σ 1 .
2.3 Instability Analysis
Instability is described as the localized, non-uniform plastic deformation that occurs prior to a material failing. This transpires when the change in force or pressure acting on the specimen is equal to zero. In uniaxial tension this phenomenon is termed necking and takes place when the change in axial force is equal to zero. This analysis focuses on the instability occurring when a cylinder or series of cylinders fail due to internal pressure. Figure 2-2 represents an idealized pressure versus strain curve as 13 experienced when a cylinder is pressurized internally. The abrupt change or decrease in pressure (instability) is the point of interest.
dP=0
Figure 2-2: Idealized pressure curve. Initial, non-linear portion of curve is due to test apparatus compliance.
From Figure 2-2, instability occurs when dP = 0 where P is given by Equation
2.6.
td dt σσσ tdr dP 11 1 =−+= 0 (2.7) r 22 r 2r 2
which can be rewritten as:
dσ dr dt 1 −= (2.8) σ 1 r t
dr dt Recognizing that = dε , = dε and for plane strain dε = 0 (where ε , ε r 1 t 3 2 1 2
and ε 3 are principal strains). Due to volume conservation in plastic deformation,
ε1 −= dd ε 3 for plane strain. 14
Equation 2.8 then becomes:
dσ 1 = 2dε1 (2.9) σ 1
From the von Mises criterion, the effective strain function for plane strain is given by:
1 2 ⎡2 2 2 2 ⎤ 2 ⎢ ()1 2 ++= dddd εεεε 3 ⎥ = dε1 (2.10) ⎣3 ⎦ 3
Rearranging yields:
3 = dd εε (2.11) 1 2
From the plane strain assumption and the plastic flow rules:
dε ⎡ 1 ⎤ dε 2 2 ()+−= σσσ 31 = 0 (2.12) σ ⎣⎢ 2 ⎦⎥
This reduces to:
+ σσ σ = 31 (2.13) 2 2
For the von Mises criterion, the plane strain effective stress σ is given by:
1 1 2 2 2 2 3 []()()()21 32 σσσσσσσ 13 (−=−+−+−= σσ 31 ) (2.14) 2 2
DP Noting thatσ = i ,σ = −P and rearranging and solving for σ in terms of 1 t 3 i 3
σ 1 , provides Equation 2.15. 15
−σ t σ = 1 (2.15) 3 2r
Substituting Equation 2.15 into 2.14 yields:
3 ⎛ σ 1t ⎞ ⎜σσ 1 += ⎟ (2.16) ⎝ 22 r ⎠
Solving Equation 2.16 for σ 1 :
2 ⎛ 2r ⎞ 1= σσ ⎜ ⎟ (2.17) 3 ⎝ 2 + tr ⎠
Differentiating Equation 2.17 and substituting the results and 2.11 into 2.9
provides Equation 2.18
2 ⎛ 2r ⎞ ⎜ ⎟dσ dσ 3 2 + tr 3 1 2dε == ⎝ ⎠ = 2 dε (2.18) σ 1 2 ⎛ 2r ⎞ 2 1 ⎜ ⎟σ 3 ⎝ 2 + tr ⎠
Which simplifies to the following stress-strain relationship at instability:
dσ = 3σ (2.19) dε
Now recalling that:
r t ε1 = ln and ε 3 = ln (2.20) ro to
where ro and to are the initial channel radius and wall thickness, respectively.
Solving Equation 2.20 for r and t: ⎛ 3 ⎞ = rr exp ε = r exp⎜ ε ⎟ (2.21) o ()1 o ⎜ ⎟ ⎝ 2 ⎠ 16
⎛ 3 ⎞ = tt exp ε t exp⎜−= ε ⎟ (2.22) o ()3 o ⎜ ⎟ ⎝ 2 ⎠
where:
3 3 = εε and −=−= εεε (2.23) 1 2 13 2
Substituting Equations 2.17 and 2.20 into 2.6 yields:
σ t 2 ⎛ 2r ⎞ t 2 ⎛ t ⎞ P 1 == σ ⎜ ⎟ = σ ⎜ ⎟ (2.24) 2r 3 ⎝ + tr ⎠ 22 r 3 ⎝ 2 + tr ⎠
Finally substituting Equation 2.25 into 2.28 gives:
2 ⎛ t ⎞ P = σ ⎜ o ⎟ (2.25) max ⎜ ⎟ ⎝ Do ()3exp3 ε + to ⎠
Equation 2.25 reflects the maximum pressure in terms of σ , ε ,to and ro . Where σ is
the effective stress, ε is the effective strain, to is the initial web thickness, and Do is the initial diameter of the channel.
Equation 2.25 can be used as a predictive model for internal pressure of micro- channel tubing. Knowing initial tube geometry (web thickness and channel diameter) and material behavior (constitutive equations) the maximum pressure can be calculated.
Initial dimensions will be presented in Chapter 3, whereas constitutive equations will be developed in Chapter 5.
17
2.4 Validating State of Stress
G. Vamadevan [10] performed a finite element analysis (FEA) to verify the effective stress induced in the internal web as a function of pressure. Using finite element software, MSC Marc, the stress distribution at the center of the internal wall was determined (Figure 2-3). Analysis conditions include using a similar tube profile with an internal pressure of 17.8 MPa (2581 psi). The FEA results are then compared to an analytical model (Equations 2.1, 2.4 and 2.16) and presented graphically in Figure 2-4.
Figure 2-3: Results of a finite element analysis on the internal wall of the micro- channel tube. The stress ranges from 68.0MPa in the center to 97.2MPa at the surface [10]. 18
100 98 96 94 From FEA analysis (Fig.2.3) 92 From Eqns. 2.1, 2.4 & 2.16 90 88 86 84 82
80 78 76 74 von Mises stress (MPa) 72 70 68 66
0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 Distance from center of channel (mm)
Figure 2-4: Stress distribution in the wall of the micro-channel shown in Figure 2-3 using finite element analysis (FEA) and Equations 1, 4 and 16 [12].
For micro-channel with a nominal diameter of 0.8 mm and a wall thickness of
0.2mm the mean stress of the FEA results is 77.7 MPa and the mean stress of the distribution calculated from Equations 2.1, 2.4 and 2.16 is 77.1 MPa. After examination of the two different analysis methods, it is shown that the edges of the wall experiences the highest stress whereas the center experiences the lowest. Additionally, differences in the overall mean stress is calculated to be 0.8%. This is reasonable enough, due to the fact that the development of the mathematical model depends directly on the mean stress. 19
Therefore, the FEA model validates the stress state experienced when the tube is internally pressurized.
20
CHAPTER 3
MATERIAL
3.1 Alloys
The materials tested in this research are two 3000 series alloys and one variant.
AA 3102 and AA 3003 are Aluminum Association designated alloys whereas 1197 is an unregistered alloy that essentially meets the AA 3102 specification plus the addition of
Copper. Table 3-1 presents the chemical composition, as determined by optical emission spectroscopy (OES), of the three alloys. Brazeway Inc., conducted all chemical analyses.
Table 3-1: Chemical composition of alloys used during experimentation (determined with optical emission spectroscopy). Alloy Alloying Element (weight %) Si Fe Cu Mn Mg Zn Ni Ti 1197 0.067 0.131 0.409 0.143 0.003 0.020 0.003 0.017 3102 0.069 0.491 0.012 0.234 0.011 0.007 0.005 0.016 3003 0.216 0.551 0.081 1.100 0.001 0.015 0.007 0.015
3.2 Tube Geometry
Prior to testing, samples from each alloy were measured under a stereomicroscope. The channel diameters and web thickness were averaged to develop a set of nominal dimensions. Table 3-2 shows the actual measurements and averages for the channel diameter and web thickness that will be used to predict burst pressure.
21
Table 3-2: Initial channel diameter and web thickness, measured from tubes of each of the 3 alloys. 1197 1197 AA 3003 AA 3003 AA 3102 AA 3102 Channel (mm) Web (mm) Channel (mm) Web (mm) Channel (mm) Web (mm) 0.43 0.409 0.433 0.395 0.434 0.421 0.415 0.427 0.423 0.432 0.409 0.441 0.416 0.437 0.421 0.443 0.423 0.413 0.423 0.444 0.418 0.437 0.433 0.442 0.416 0.426 0.424 0.428 0.411 0.434 0.405 0.448 0.422 0.433 0.44 0.442 0.408 0.423 0.423 0.408 0.407 0.422 0.432 0.433 0.408 Average 0.418 0.431 0.425 0.425 0.421 0.431
3.3 Sample Profile
Figure 3-1 is a sketch showing nominal dimensions of the micro-channel tube
used in this research.
7.56 mm 1.20 mm 0.60 mm 0.44 mm
0.41 mm
0.60 mm
Figure 3-1: Sketch of experimental R744 tube profile used during experimentation.
22
3.4 Manufacturing and Handling Processes
During the manufacture of multi-channel tubing, the material undergoes various microstructural changes. The tube initially goes through a hot extrusion process to create the near net shape geometry. Following this process is the straightening and sizing operations. These handling processes induce a small amount of cold work on the tube that in return alters its mechanical properties [13].
3.4.1 Hot Extrusion of Micro-Channel Tube
Extrusion is widely used throughout industry to produce parts of complex geometry and uniform cross-section. This process begins with a high quality homogenized aluminum alloy billet. The heated billet is placed inside the container of a direct/indirect extrusion press. The billet is then forced through a die opening by a hydraulic ram. The long, straight tube exits the opposite side of the die where it is wound onto coils, due to the continuous nature of the extrusion process. The coiled tube is sent to be further processed and assembled.
3.4.2 Material Handling and Roll Sizing
The long, coiled tube is now straightened and cut to final length. From the coiled roll, the tube is processed through a series of rollers to produce long, straight parts. The straight pieces are then run through another sequence of rollers to generate parts that have precise external dimensions. Finally the tubes are cut to length and are ready to be 23 assembled into parallel flow heat exchangers. Tube samples processed to this extent were obtained for testing.
24
CHAPTER 4
EXPERIMENTAL PROCEDURE
4.1 Simulated Brazing Cycle
During the manufacture of parallel flow heat exchangers, the entire assembly undergoes a brazing cycle in order to join the individual components. The micro-channel tubing is inserted into the heat exchanger’s two headers and thin fins are inter-woven between the many tubes (see Figure 4-1).
Figure 4-1: Standard automotive parallel flow heat exchanger [6].
A cladding alloy, which has a melting point about 80oC lower than the tube alloy, is present on the headers and fin stock prior to brazing. The entire assembly is introduced to an oxygen free, nitrogen rich furnace at 600-605oC (approximately 94% of the melting point of aluminum). Within this environment, it undergoes controlled atmosphere 25 brazing or NOCOLOK® brazing [14]. At approximately 560oC the flux melts, dissolving the oxide layer from the aluminum alloy surface, wetting the component surface, allowing the cladding material to be drawn into the joints due to capillary flow [15].
Upon cooling, the joints that are obtained are stronger than the parent material.
4.2 Effects of Brazing
Subjecting aluminum alloys to these thermal cycles can result in significant changes in mechanical properties. Specifically, the microstructure is altered due to the amount of prior deformation experienced during other manufacturing processes
(straightening, sizing and material handling). The amount of cold work induced during these processes is the driving force for recrystallization and grain growth during brazing
[7].
Each of the three alloys possessed pre-braze grain size of 50-100 µm, which is typical of hot extruded aluminum micro-channel tube. However, post-braze microstructure differed vastly from one alloy to the next. The 1197 underwent total recrystallization resulting in very large grain structure throughout the tube (Figures 4-2 &
4-3). Whereas the 3102 alloys only recrystallized in the interior walls, creating a composite of fine and course grain structure (Figures 4-4 & 4-5). This is a result of the roll sizing operation, concentrating strain at the tube’s web center, creating nucleation sites for grain growth. The metallography of the 3003 alloys (Figure 4-6 & 4-7) illustrates that no recrystallization is experienced. This is most likely due to the higher
Mn content, which would result in a greater number of Al6(Fe,Mn) submicron particles 26 that retard recrystallization by pinning subgrain boundaries and slowing subgrain coalescence [16]. The presence of these metallurgic changes reduces mechanical properties such as strength and ductility.
Figure 4-2: 1197 in pre-braze condition.
27
Figure 4-3: 1197 in post-braze condition.
Figure 4-4: 3102 in pre-braze condition.
28
Figure 4-5: 3102 in post-braze condition.
Figure 4-6: 3003 in pre-braze condition.
29
Figure 4-7: 3003 in post-braze condition.
4.3 Tube Furnace
In this research, a typical brazing cycle was simulated in a Thermolyne 21100 tube furnace, reconfigured with a digital Love temperature controller (Figure 4-8). 30
Figure 4-8: Thermolyne tube furnace and Love controller used for simulated brazing cycle.
The furnace was allowed to reach a steady-state temperature before any heat treatment was performed (usually about an hour). The experimental setup accepts two samples at a time, with actual temperature being monitored by three K-Type thermocouples (see
Figure 4-9). The operation was monitored with an Iotech USB data acquisition module, which displays thermocouple temperatures to a computer screen (Figure 4-10)
31
Figure 4-9: Tube holder with two samples, and equipped with three thermocouples on a dummy sample.
Figure 4-10: Thermocouple temperatures displayed to computer monitor.
32
4.4 Simulated Thermal Procedure
With the furnace at steady-state temperature, the loaded two-sample holder is placed inside the furnace. Temperature is monitored until 598oC is reached at the middle thermocouple (due to the temperature gradient within the furnace). The samples then remain at the elevated temperature for 2 minutes. During the 2 minutes, the middle thermocouple will reach approximately 605oC, whereas the end thermocouples will only experience 600oC. The tubes are then removed from the furnace and are allowed to air cool to room temperature. This concludes the simulated brazing process. The samples are then ready to be tensile tested and/or pressure tested.
4.5 Development of Constitutive Equations
Constitutive equations for each alloy in the post brazed condition, were determined from tensile test data. Prior to tensile testing, physical measurements were taken of each specific test specimen. These dimensions are presented in Table 4-1.
Table 4-1: Initial measurement of tensile specimens. Alloy Sample Mass (g) Length (mm) Area (mm2) 1 4.31 230.10 6.86 1197 2 4.31 229.95 6.87 3 4.31 229.92 6.87
1 4.38 229.87 6.98 AA 3003 2 4.38 229.87 6.98 3 4.38 229.95 6.98
1 4.35 229.95 6.93 AA 3102 2 4.34 229.84 6.92 3 4.35 229.95 6.93
33
Mass was determined using a digital laboratory scale, and length was measured with dial calipers. Cross-sectional area was determined with Equation 4.1.
m A = (4.1) ρl
Where A is area, m is mass, l is length and ρ is the density of aluminum. Density values for alloys 3003 and 3102 were taken from reference [17] (2.73 g/cm3 and 2.71 g/cm3 respectively) and the density for 1197 was estimated at 2.72 g/cm3. This measurement of area is used to determine the effective strain at instability, (discussed later herein). 34
4.6 Tensile Testing
With these initial geometric properties recorded, the tensile testing can now be initiated. Using a Tinius Olsen 1000 tensile testing machine integrated with an Iotech
USB data acquisition module, the samples were loaded into the upper jaw (Figure 4-11).
Figure 4-11: Tensile test apparatus with extensometer.
The measured force was then zeroed on the apparatus as well as on the data acquisition system. The bottom of the sample was then loaded into the lower jaw. This induces a small compressive force on the specimen, hence the prior force zero (Figure 4-12). The extensometer is then placed on the sample and the retaining pin removed.
35
Figure 4-12: Data acquisition’s home screen, reflecting a compressive force.
Next the crosshead speed was calculated in order to satisfy standard tensile testing strain rates (10-2 to 10-4 sec-1) [18].
dl
dε lo 1 dl v ε& ==== (4.2) dt ldt o dt lo
Where v is the crosshead speed, lo is the length between the jaws and ε& is the
-1 -2 -1 strain rate (sec ). Using a strain rate (ε& ) of 10 sec , a crosshead speed (v) of 1.67 mm/sec and Equation 4.2, a distance of 167 mm is needed between the jaws to create the required strain rate. 36
With the sample in place and the apparatus, with data acquisition, configured properly the test was performed on 3 samples of each of the 3 alloys. After the tests were completed, the grain structure of the 1197 and 3102 alloys became visible (see Figure 4-
13).
Figure 4-13: Visible “tree bark” like grain structure of the post-tested tubes.
These results are not significant to the tensile test outcomes, but suggest other interesting and noteworthy material characteristics. The unvarying grain structure implies that the prior thermal (brazing) cycle was carried out in a uniform manner. This also validates that the samples underwent recrystallization and significant grain growth during the brazing simulation. 37
With all of the samples tested, physical measurements were once again taken in order to determine strain at instability. Sections of the deformed specimens were cut from the tested samples. The sections were taken far enough from the instability and gripper regions to ensure that the samples were uniformly deformed. Mass and length measurements were then taken of the uniformly, plastically deformed sections. (Table 4-
2)
Table 4-2: Final dimensions of the deformed samples. Alloy Sample Cut Length (mm) Mass (g) Area (mm2) 1 138.23 2.21 5.86 1197 2 126.14 1.96 5.69 3 137.18 2.18 5.82
1 139.06 2.21 5.82 AA 3003 2 137.8 2.14 5.69 3 138.97 2.18 5.75
1 88.3 1.41 5.85 AA 3102 2 86.74 1.4 5.91 3 136.48 2.06 5.53
The final area was once again indirectly calculated using Equation 4.1.
4.7 Room Temperature Static Burst Testing
Room temperature burst testing was performed to validate the model and constitutive equations developed from the uniaxial tensile testing. The tests were conducted using the testing station integrated with the computer controlled MTS machine. 38
4.7.1 Test Apparatus
Tube samples in the post-brazed condition were burst tested to validate the analytical model developed earlier in this research. An MTS machine incorporated with a burst test station was used to perform the experimentation, Figure 4-14.
Figure 4-14: Computer controlled MTS machine and burst testing station.
The test apparatus as well as all hydraulic components are rated for pressures to 69 MPa
(10,000 psi). The internal pressure (within the tube) is developed when the single acting high-pressure hydraulic cylinder is compressed between the crosshead and ram of the servo hydraulic MTS machine. A water/rust preventative mixture is the working fluid used to generate the pressure. The system is computer controlled using object oriented 39 programming within the Multipurpose Testware (MTS software). Once the tube is loaded and the program is initiated, the operator has no responsibilities until failure occurs. At this time the failed tube is removed and replaced with a new sample wherein the test can be repeated.
4.7.2 Room Temperature Experimental Set-up
Figure 4-15 depicts the experimental set-up used during burst testing and elevated temperature burst testing.
Ball Valve #2
Ball Valve #1
Toggle Switches 1,2 & 3
Quick-disconnects
Figure 4-15: MTS machine and components of the burst testing station.
40
First, toggle switch 1 is activated, releasing the collets that secure the tube. The tube is loaded into the quick-disconnect test fixtures and the switch is switched back to lock the sample into place, Figure 4-15. Toggle switch 2 is then activated, allowing fluid to gravity feed from the reservoir into the air-operated charge tank (the switch is reversed closing the solenoid valve when the tank is full) Figure 4-16.
Control Valve
Fluid Reservoir
Charge Tank
Figure 4-16: Selected components of burst test apparatus.
Toggle switch 3 is now activated, pressurizing the charge tank with line pressure
(~0.5 MPa), which in return primes the entire system with fluid. Ball valve #1 is slightly opened in order to bleed any air from within the tube. When the visible air bubbles subside, the valve is closed. Ball valve #2 is opened similarly to bleed the air from the 41 hydraulic hose. Once all air is evacuated from the system and all valves are closed, the three-way control valve is turned to the testing position. The tube is now loaded and ready to be tested.
4.7.3 MTS Room Temperature Test Procedure
The remainder of the procedure is performed in Station Manager (MTS software).
Figure 4-17 illustrates the burst test procedure used during the room temperature testing.
Figure 4-17: Room temperature burst testing procedure.
Process 1 applies parameters for timed data acquisition. This step defines the signals to be recorded, destination folder name, and the rate of data acquisition. It is initiated when the procedure is started. Process 2 is a ramp command that defines the rate at which the ram will apply force to the hydraulic cylinder. Process 2 is also initiated when the procedure is started. 42
Process 3 is a failure detection command. This action will terminate process 2 when a 10% reduction of internal pressure is experienced within the pressure transducer.
The final process (4) simply brings the ram back to its home position, where the hydraulic cylinder is fully extended.
4.8 Improving Elevated Temperature Burst Testing
Prior to any elevated temperature testing, the process in which the tubes were heated was improved.
4.8.1 Upgrading Convection Heater
During normal operating conditions, a parallel flow heat exchanger will experience temperature fluctuations. To simulate these elevated temperatures, a forced- air convective resistance heating system was developed. The heater used was an Omega
1200-watt low flow air process heater, Figure 4-18. Compressed air was passed over the resistance heating elements in order to increase the temperature of the tube. 43
Compressed air inlet
Heated region Heater
Figure 4-18: Omega forced-air convective resistance heater.
The heater has an enclosed heating surface, which allows protection from liquid splash when failure transpires. Combining 1200 watts of heating power with a barrier between the resistance heating elements and the working fluid, this heater minimized the heating time. Thus, the overall experiment time for each test is decreased.
4.8.2 Improving Temperature Control
Inducing internal pressure within the test tube, via the MTS machine, is precisely controlled by its computer system. The same trouble-free, accurate control can be applied to the elevated temperature testing. A communication line between the MTS software and a Eurotherm 2216e temperature controller was established. 44
The controller was wired, in conjunction with a solid-state relay and the heater, to open a communication link between the MTS software and the Eurotherm unit.
Feedback of the temperature signal to the controller is a K-type thermocouple, connected directly to the sample tubes surface. The controller and the MTS software were reconfigured to accept this new arrangement.
A new station was developed in Station Manager software to recognize the new temperature input in addition to configuring the output signal from the computer to the controller. Baud rates, signal addresses, and upper and lower temperature limits were adjusted to coincide with the settings within the temperature controller.
A new test procedure (Figure 4-19) was developed to reflect the system changes and incorporate the new controller for hassle free operation. Once the tube sample is ready to be tested, the operator starts the procedure and the computer takes control of the experiment.
4.9 Elevated Temperature Burst Testing
The room temperature testing was supplemented with elevated temperature burst testing in order to quantify burst reduction as a function of temperature. The tubes were tested at 60, 120 and 180oC.
4.9.1 MTS Elevated Temperature Test Procedure
With the convection heater and temperature controller improved, elevated temperature testing could be carried out more efficiently and with less human error. A 45 new elevated-temperature MTS test procedure was executed at 3 additional temperatures
(60, 120 and 180oC) in order to quantify the reduction of burst pressure as a function of temperature. Figure 4-19 depicts the new MTS test procedure developed for the elevated temperature burst testing. This procedure reflects the new temperature control command.
Figure 4-19: Elevated temperature burst testing procedure.
Process 1 applies parameters for timed data acquisition. This step defines the signals to be recorded, destination folder name, and the rate of data acquisition. It is initiated when the procedure is started. Process 2 is a ramp command that induces an internal pressure (within the tube) of 2.07 MPa (300 psi). This is required in order to prevent the fluid inside the tube from boiling due to the applied heat. Process 2 is also initiated when the procedure is started. 46
Process 3 is the heating command. This process changes the set point on the
Eurotherm controller to the desired temperature. As the temperature begins to ramp to the specified value, the power given to the heater is automatically adjusted accordingly to prevent overshoot. The parameters set within this command are the tolerance limits
(± 2o C) and the dwell period, the time the temperature must stay within the tolerance limits before the next process will start, (5 seconds). Once again this process starts at the beginning of the procedure.
Process 4 is a ramp command that defines the rate at which the ram will apply force to the hydraulic cylinder. This process is executed when the tube is at the appropriate temperature. Process 5 is a failure detection command. This action will terminate process 4 when a 10% reduction of internal pressure is experienced within the pressure transducer. After failure is detected, process 6 changes the set point on the temperature controller back to 20o C. Finally process 7 simply brings the ram back to its home position, where the hydraulic cylinder is fully extended. 47
CHAPTER 5
RESULTS AND DISCUSSION
5.1 Tensile Testing Results
Figure 5-1 depicts the tensile test results of three 1197 alloys tubes in the post-
brazed condition.
100 14.5
80 11.6
60 8.7 (MPa) σ kpsi
40 5.8
Stress, Test 1 Test 2 20 2.9 Test 3 -2222ε -13.88ε σ = -7.70e -83.88e +101
0 0.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 Strain, ε
Figure 5-1: 1197 tensile testing data for 3 samples fitted with a 2nd order exponential function. Empirical exponential function was numerically determined with Origin plotting software.
48
5.1.1 Alloy 1197 Constitutive Equation
In uniaxial tension the constitutive equation relating effective strain to effective stress at instability can be given by:
dσ = σ (5.1) dε
where σ is effective stress and ε is effective strain.
Differentiating the effective stress equation (with respect to effective strain) given by the
2nd order exponential function, given in Figure 5-1, and equating it to the effective stress equation yields the effective strain at instability.
dσ = 40.17109 e − ε )2222( + 25.1164 e − ε )88.13( σ −== 70.7 e − ε )2222( − 88.83 e − ε )88.13( +101 dε
Numerically solving the above equation yields:
ε = 181.
where ε is the effective strain at instability for alloy 1197.
49
5.1.2 AA 3003 Constitutive Equation
Figure 5-2 shows the AA 3003 alloy tensile testing data. These samples deformed alloy in such a manner that a standard power law hardening function could be used in describing its behavior. Similarly, Equation 5.1 can be applied to the model to calculate the effective strain at instability. This results in an effective strain at instability for AA
3003 equal to ε = 178. .
140 20.3
120 17.4
100 14.5
80 11.6 (MPa) σ Test 1 kpsi 60 Test 2 8.7 Test 3 Stress, .21 40 σ = 187ε 5.8
20 2.9
0 0.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 Strain, ε
Figure 5-2: AA 3003 tensile testing data for 3 samples fitted with power law hardening model. 50
5.1.3 AA 3102 Constitutive Equation
Illustrated in Figure 5-3 are the results to tensile testing three AA 3102 specimens. Once again this data is approximated by a 2nd order exponential decay function. The effective strain at instability is again calculated using Equation 5.1 (ε = 210. ).
The models used to predict instability strain in uniaxial tension do so very accurately. As seen when compared to their respective data sets, the results vary only slightly. These functions can now be used for the basis of the predictive models related to burst testing. 51
100 14.5
80 11.6
60 8.7 (MPa) σ kpsi
40 5.8
Stress, Test 1 Test 2 20 Test 3 2.9 -11.88ε -144.3ε σ = -61.88e -29.13e +96.42
0 0.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 Strain, ε
Figure 5-3: AA 3102 tensile testing data for 3 samples fitted with a 2nd order exponential function. Empirical exponential function was numerically determined with Origin plotting software.
5.2 Uncertainty Analysis
An uncertainty analysis was performed to validate the accuracy of the indirect method (Equation 4.1) used to measure initial and final cross-sectional area of the tubes.
1 ⎡ 2 2 2 ⎤ 2 ω ⎛ ωρ ⎞ ⎛ ω ⎞ ⎛ ω ⎞ A = ⎢⎜ ⎟ + ⎜ L ⎟ + ⎜ m ⎟ ⎥ (5.2) A ⎜ ρ ⎟ mL ⎣⎢⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎦⎥ 52
ω Where A is the relative uncertainty of the area, ω is the uncertainty of the A ρ
3 density (±0.01g/cm ), ωL is the uncertainty of the length (±0.01mm), and ωm is the uncertainty of the mass (±0.01g). Making the appropriate substitutions into Equation 5.2 yields a relative uncertainty in cross sectional area of 0.4 %.
5.3 Tube Failure
Figure 5-4 shows the before and after views of the cross-sectional area of the multi-channel tubing.
Figure 5-4: Cross-sectional view of multi-channel tubing before and after failure.
53
As seen in Figure 5-4, the tube clearly fails at several internal webs prior to fully rupturing. It is obvious that the maximum stress occurs at the internal web versus the exterior wall. This result validates the assumptions made earlier in developing the predictive mathematical model as well as giving designers insight to where the geometry is most critical.
5.4 Room Temperature Analysis
Three samples of each of the three aluminum alloys, in the post brazed condition, were burst tested at room temperature. An additional 7 samples of the 1197 alloy were tested in order to perform a statistical study. A typical burst pressure versus ram displacement response can be seen in Figure 5-5.
54
inches 0.00 0.20 0.39 0.59 0.79 0.98 1.18 1.38 50 7.26
40 5.81
30 4.35
20 2.90 kpsi
Test Pressure (MPa) 10 1.45
0 0.00 0 5 10 15 20 25 30 35 Ram Displacement (mm)
Figure 5-5: Typical test pressure versus ram displacement curve.
Burst pressures were recorded and averaged for each set of the alloys (Table 5-1). A maximum pressure, for each alloy, was calculated using the predictive mathematical model. Knowing the effective stress in terms of the effective strain (the constitutive equations developed earlier in this chapter) and the initial dimensions of the tube (web thickness and channel diameter) the maximum pressure expected was determined. These results were compared to the average burst pressures measured during the experimentation (Table 5-2).
55
Table 5-1: Measured (actual) burst pressures, of the three alloys, at room temperature. 1197 (MPa) 3003 (MPa) 3102 (MPa) 45.15 64.27 39.80 46.47 64.52 41.05 46.39 64.46 40.79 45.31 45.96 46.12 46.96 46.91 45.70 45.79 Average 46.08 64.42 40.54
Table 5-2: Predicted burst pressures at room temperature and percent differences from the actual, measured values. 1197 (MPa) 3003 (MPa) 3102 (MPa) 46.15 62.06 43.08 % Difference 0.2% 3.7% 6.2%
5.5 Statistical Analysis
Ten samples of alloy 1197 were burst tested at room temperature with the purpose of determining the variability in the testing process and material. The significance of this study is to demonstrate the degree to which the data represents the overall population of test samples. Using the 1197 maximum pressure values in Table 5-1 and a sample size of
10, a standard deviation of 0.615 MPa (89.2 psi) was calculated. When comparing the standard deviation to the values in Table 1, it can be determined that seven of the 10 pressures fall within one standard deviation from the mean, whereas the other three values fall within 2 standard deviations. These 10 values are encompassed within a 56
95.5% confidence interval (46.08 ± 1.23 MPa). In other words, we are 95.5% confident that this specific interval will contain all data points pertaining to this particular experiment. Given these results, it can be assumed that 3 samples of each alloy will sufficiently characterize the sample population.
5.6 Elevated Temperature Testing Analysis
As temperature increases, mechanical properties such as yield strength diminish.
Figure 5-6 shows failure pressure plotted as a function of tube temperature.
65.50 9.5
62.05 1197 9.0 AA 3003 58.60 AA 3102 8.5 55.16 8.0
51.71 7.5
48.26 7.0
44.82 6.5 kpsi 41.37 6.0
Pressure (MPa) 37.92 5.5
34.47 5.0
31.03 4.5
27.58 4.0
0 20406080100120140160180200 Temperature (C)
Figure 5-6: Burst pressure as a function of temperature for all 3 alloys.
57
Figure 5-6 illustrates that burst pressure decreases linearly as the test temperature increases. With this data, a linear burst pressure reduction per Celsius (r) was determined for each alloy (Table 5-3). Elevated temperature failure pressure can then be assessed, as a function of test temperature, using room temperature and failure pressure at room temperature as reference values.
Table 5-3: Reduction values per C, determined from data presented in Figure 5-6. Alloy reduction, r (C-1) 3102 0.0017 1197 0.0012 3003 0.0016
Equation 5.3 can then be used to predict the burst pressure (pburst) at elevated temperatures (between 20 oC and 180 oC).
burst = 0 [1 − ( − TTrpp 0 )] (5.3)
o where p0 is the burst pressure at room temperature (∼22 C), r is the reduction per
Celsius, T is the temperature in Celsius and T0 is room temperature in Celsius. Figure 5-
7 depicts the actual measured elevated temperature burst pressures as well as the predicted values. The predicted values were plotted as a function graph, using Equation
5.3 with the appropriate substitutions. Equation 5.3 predicts elevated temperature burst pressures within ~8% of the actual measured values. 58
65.50 1197 9500 62.05 AA 3003 9000 AA 3102 58.60 p=p [1-r(T-T )] 8500 o o 55.16 8000
51.71 7500
48.26 7000
44.82 6500 psi 41.37 6000
Pressure (MPa) 37.92 5500
34.47 5000
31.03 4500
27.58 4000
0 20 40 60 80 100 120 140 160 180 200 Temperature (C)
Figure 5-7: Actual elevated temperature failure pressures and predicted values, using Equation 5.3, for each of the 3 alloys.
59
CHAPTER 6
CONCLUSIONS
The conclusions to all experimentation and analysis covered in this research are presented in this chapter. Also presented are relative recommendations for future work.
6.1 Conclusions
In this research, an analytical model was developed to predict failure pressure in aluminum micro-channel tubing used in automotive parallel flow heat exchangers. The model predicts room temperature failure pressure as a function of material properties and dimensions to within 6% of experimental test values. This study also derived a model to calculate burst pressure at elevated temperatures of the same tubing to within 8% of the actual measured values.
As the push for environmentally friendly refrigerants becomes prominent, engineers must seek solutions to the mechanical performance demand associated with these new refrigerants (i.e., CO2). As CO2 based climate control systems gain acceptance in the automotive world, new design criteria as well as innovative materials must be examined. This thesis studies the aluminum micro-channel tubing used in the manufacture of automotive, parallel flow heat exchangers. Specifically, it presents an analytical model to predict the failure pressure of micro-channel tubing at system operating conditions. The model uses the material’s stress-strain relationship
(constitutive equation), which was obtained through uniaxial tensile testing. This model was then validated by a series of static pressure tests using alloys 1197, AA 3003 and AA 60
3102. Elevated temperature static burst tests were conducted to further understand material behavior at higher temperatures (60, 120 and 180oC), within the range of gas cooler operation.
• A mathematical model was developed and extended to predict room temperature
failure pressure in micro-channel tubing used in automotive parallel flow heat
exchangers. The model indicates pressure as a function of effective stress σ ,
effective strainε , initial web thickness to and initial channel diameter Do .
During pressure testing, failure occurs at one or more internal walls, and the
maximum pressure corresponds to instability in the walls. The instability strain,
for this stress state, is predicted with this model. The analytical expression
predicts failure pressure to within 6% of the experimental data.
• To validate the mathematical model presented earlier herein, material behavior for
the tubes in the post-brazed condition was determined. Three samples of each of
the 3 alloys (1197, AA 3003 and AA 3102), in the post-brazed condition, were
tested in uniaxial tension. Instability strain and failure stress were measured,
plotted and averaged in order to establish a constitutive equation for each alloy.
• Failure pressures at room temperature (~22oC) for each alloy were compared to
the analytical model. The predicted burst pressure of alloy 1197 was within 0.2%
of the actual measured burst pressure. The AA 3003 and AA 3102 alloys had
discrepancies of 3.7% and 6.2%, respectively. The 95% confidence interval for 61
pressure tests was (46.08 ± 1.23 MPa). This was determined with 10 room
temperature tests of 1197 alloy samples.
• An analytical model was developed to predict failure pressure at elevated
temperatures (up to 180o C). Three samples of each of the 3 alloys, in the post
brazed condition, were ruptured at 60, 120 and 180o C. A linear regression was
performed on the elevated temperature static burst pressure data. Both the
experimental values and predicted values were compared. The model predicts
failure pressure, as a linear function of test temperature, to within 8% of the actual
measured values.
6.2 Future Work
The most significant part of this research was to validate the predictive, mathematical model with a series of static burst tests. This will allow designers to easily design heat exchangers based on the predictions of the model, given the initial tube geometry and material behavior (constitutive equations). In order for the model to accurately calculate maximum burst pressure, precise material behavior must be developed. This suggests that the means by which the constitutive equations are developed needs to be improved for elevated temperature conditions.
This research developed constitutive equations through room temperature, uniaxial tensile testing; however, these equations are most accurate when applied to the room temperature burst testing. For the elevated temperature conditions, elevated 62 temperature tensile testing should be implemented. This will account for the diminishing mechanical properties due to increasing working temperature.
Another critical factor in predicting maximum burst pressure expected within micro-channel tubing is its physical dimensions. To further confirm the consistency of the model’s ability to estimate burst pressure, tube dimensions should be varied. A range of physical dimensions should be applied to the analytical model and validated by another series of burst tests. By altering all of the variables within the analytical model
(i.e. channel diameter and web thickness), this will insure that the model’s ability to predict burst pressure will be challenged.
63
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[1] W. Stadmüller, R. Cäsar, “Material Related Design Criteria and Test Methods for Components Driven by R744 as Refrigerant” 2000 SAE Automotive Alternative Refrigerant Symposium, July 11-13, Scotsdale, AZ
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[6] Unpublished Photo by Frank Kraft
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[13] F.F. Kraft, H.R. McCarbery, J.C. Novesky, “Metallurgical Aspects of Extruded and Brazed Materials”, Proceedings of the 1999 International Invitational Aluminum Brazing Seminar, October 26-28, 1999, Dearborn, MI, (Therm Alliance, Wixom, MI)
[14] “Controlled Atmosphere Brazing Furnace Systems-The Theory”, Product bulletin, SECO/WARWICK Corporation
[15] “Equipment Used In The Controlled Atmosphere Brazing Of Aluminum Heat Exchangers”, Forni-Tecnica s.r.l., page 3
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[18] S. Kalpakjian, S.R. Schmid, Manufacturing Processes for Engineering Materials, 4th Edition, Pearson Education, Inc., 2003, p.39