ASE 324L Aerospace Materials

ASE 324L Aerospace Materials Lab #9 Fracture Toughness Testing

Instructor: Dr. Kenneth M. Liechti TA: Liang-Hai Lee Lab Session 3

Robin Prosser

9 November 2001 ABSTRACT

Twelve 2024-T3 Aluminum specimens of varying thicknesses (0.125, 0.25, 0.5 inches) were subjected to Fracture Toughness Tests in the W.R. Woolrich Laboratories of the University of Texas at Austin. Each specimen contained a preexisting crack and then underwent tensile loading to complete fracture. The responsive load and displacement of each specimen were measured. The average Fracture Toughness, Kc, was calculated for each thickness. The 0.125-in specimen demonstrated the superior Kc of 44.65 ksi-in0.5. Next came the 0.5-in specimen at Kc = 37.32 ksi-in0.5, followed by the 0.5-in specimen at Kc = 36.62 ksi-in0.5. These results confirm that Fracture Toughness increases with decreasing thickness. Results also confirmed that the initial crack length had no effect on fracture toughness. The applications of this information to everyday engineering problems are innumerable. 1.0 INTRODUCTION

Twelve Aluminum specimens of varying thickness were subjected to fracture toughness tests to determine each specimen’s resistance to fast fracture. The importance of such tests becomes immediately obvious with the phrase “resistance to fast fracture.” This material quality is of vital importance when selecting materials for aerospace structures , or any structure, within a specified operating realm.

What material property describes this “resistance to fast fracture?” We define the Stress Intensity Factor, K, having units ksi-in1/2. The stress intensity factor for every material, whether in normal or shear stress, adheres to the basic form:

K =s pa ҙ Q(a) (1)

Where K = Stress Intensity Factor

 = Stress (x, y, or xy,) a = crack length Q(a) = Correction Factor for Varying Geometries

Equation (1) shows that K is a function of loading (stress, ) and geometry (crack length, a) only. K = K(, a)

The onset of fast fracture is given by the critical stress intensity factore, or Fracture Toughness (Kc). This material property is then added to the list of important material properties such as Young’s Modulus, Poisson’s Ratio, yield strength, etc. Fracture Toughness allows us to predict the stress level for fast cracking for a fixed crack length. Inversely, for a fixed stress level, it allows us to predict how long a crack can grow before the onset of fast fracture. Hence the importance of fracture toughness testing to determine this useful property. K = Kc Fracture Toughness Property When (K < Kc) ….. Safe Operating Conditions (K = Kc) ….. Crack Begins, Propagates (K > Kc) ….. Onset of Fast Fracture

2.0 EXPERIMENTAL AND DATA REDUCTION PROCEDURES

2.1 Apparatus

This lab performed fracture toughness tests on twelve separate 2024-T3 Aluminum specimens of varying thickness, b (0.125, 0.25, 0.5 inches). Each specimen contained a preexisting crack of length a, accomplished through cyclic loading prior to this experiment. To accomplish the toughness tests, we subjected each specimen to tensile loading, causing the crack to propagate and ultimately result in fracture. The Instron loading device measured the reactive load, P, and the applied displacement, , and displayed the data in realtime on a personal computer.

P, 

Al Specimen of Thickness, b  Crack Faces x

Crack Geometry

2.2 Data Reduction

Twelve Aluminum specimens with preexisting cracks were subjected to tensile loading until failure. Table 1 lists the geometry of each specimen.

Table 1: Specimen Geometries Specimen Thickness, b Width, W Crack Length, a X No. [inches] [inches] [inches] [a/W] 1 0.125 1.936 0.827 0.427169 2 0.125 1.944 0.984 0.506173 3 0.125 1.925 1.052 0.546494 4 0.125 1.931 0.990 0.512688 5 0.250 2.023 0.924 0.456747 6 0.250 1.935 0.990 0.511628 7 0.250 1.942 0.982 0.505664 8 0.203 1.942 1.107 0.570031 9 0.500 1.953 1.003 0.5137 10 0.500 1.942 0.990 0.509784 11 0.500 1.947 1.083 0.55624 12 0.500 1.942 1.105 0.569001 By plotting graphs of Load (P) vs. Displacement (), it was possible to extract the critical load (Pc) as the maximum load experienced by the specimen (Fig 3 – 5). Armed with this value for Pc and the specimen geometries in Table 1, it becomes possible to calculate the fracture toughness (Kc) with the following equation:

P a K = f (x), where x = b W W P K = c 29.6x1/2 - 185.5x 3/2 + 655.7x5/2 - 1017x7 /2 + 639x9 /2 (2) c b W [ ] (Applicable when 0.45 Ј x Ј 0.55)

Each calculated fracture toughness, Kc, was then plotted against crack length, a, and thickness, b, (Fig 1 and 2) to determine relationships between fracture toughness and specimen geometry.

The American Society for Testing of Materials (ASTM) provides criteria to determine whether the Kc determined in the test is indeed the plane strain fracture toughness, K1C.

2 жK ц If a,c 2.5з c ч і з ч иs ys ш (3) Then Kc = K1c

Through examination of the linear portions of each specimen’s Load versus Displacement graph (Fig 6 – 17), we were able to extract the material’s Compliance value, C.

D йinch щ C = = к ъ (4) P лк kip ыъ

This experiment also involved calculating the maximum stress a 10’x10’x0.1” steel plate containing a two-inch crack can withstand before that crack will propagate. The yield stress and K1C were already known. This calculation was accomplished with the Equations 1 and 5, below.

a x = = 0.01667 W

2 3 4 a f (x) =1.12 - 0.23x +10.62x - 21.7x + 30.4 x =1.1190 (5) Steel Plate: K1c  =185 ksi s c = ys pa f (x) K =50 ksi-in0.5 1C s c =17.83 ksi

3.0 RESULTS AND DISCUSSION

The calculated results from the fracture toughness tests are summarized in Table 2.

Table 2: Experiment Results Specimen Critical Fracture Average ASTM Compliance,C Plastic Zone

No. Load,Pc Tougness, Kc Kc Criterion Kc = K1c? Size, rp [kips] [ksi-in0.5] [ksi-in0.5] [in/kip] [inches] 1 1.07 48.30025 44.65537784 1.795101888 No 0.058661 0.11428 2 0.7581 42.57464 1.394736826 No 0.038927 0.088792 3 0.6856 44.01542 1.490733531 No 0.045017 0.094903 4 0.7608 43.7312 1.471543265 No 0.044693 0.093681 5 1.602 38.27012 37.32256408 1.126963768 No 0.023538 0.071745 6 1.319 37.74602 1.096308092 No 0.025015 0.069793 7 1.255 35.2041 0.95362309 No 0.027235 0.06071 8 0.8907 38.07002 1.115209479 No 0.035286 0.070996 9 2.762 39.5946 36.62205927 1.206319073 No 0.014937 0.076797 10 2.786 39.56762 1.204675886 No 0.014294 0.076692 11 1.686 27.82187 0.595611104 No 0.014951 0.037918 12 2.285 39.50415 1.200813987 No 0.015624 0.076446

Figure 1 displays the relationship of Kc versus crack length, a. The lines do not reveal any noticeable trends between the two values for any thickness. Therefore, it can be surmised that fracture toughness does not depend on initial crack length.

Figure 2 plots the fracture toughness as a function of thickness, b. It shows that the average fracture toughness increases with decreasing thickness. In short, the material gets tougher as it becomes thinner.

The ASTM criterion value was calculated for each specimen to determine if the calculated Kc was indeed the plane strain fracture toughness K1C. No specimen passed the criteria for K1C.

Compliance values for each thickness were plotted against crack length in Figure 18. This graph showed no relationship between crack length and compliance. However, the graph did show that compliance values increase with decreasing thickness.

An examination of the fracture surface of each specimen showed rough flat fracture in the middle with shear lips on the edges. A material under plane strain (such as in our experiment) will result in flat fracture. A specimen subjected to plane stress will result in slant fracture, e.g. a fracture surface slanted at an approximately 45-degree angle. Shear lips are examples of slant fracture. This phenomenon occurs because as the fracture surface approaches the edges of the specimen, the specimen’s relative thickness decreases. So at the edges, the thick specimen behaves as a thin specimen, and plane stress takes over. Hence, the slant fracture shear lip brought on by plane stress. The maximum stress for the steel plate was determined in Section 2.2 to be 17.38 ksi. This value is conservative because it was calculated with the ASTM-approved K1C, which provides a conservative measure of fracture toughness to ensure material operation with safe parameters.

4.0 CONCLUSIONS

Results from the fracture toughness testing of twelve 2024-T3 Aluminum specimens confirmed an important trend in material properties: fracture toughness and compliance increase with decreasing thickness. The value of this knowledge to the engineering field is unquestionable. Graphs showed no effect of the initial crack length on either fracture toughness or compliance.

To summarize, when designing structures based on compliance and fracture toughness, one should carefully examine material thickness and the stresses to be applied. The indifference of compliance and fracture toughness with respect to initial crack length confirms that crack propagation is not a threat as long as the applied stress remains below critical levels (e.g. K < Kc).