Fracture Behavior of Bulk Crystalline Materials

1. Fracture Behavior of Bulk Crystalline Materials • Rice’s J-Integral • As A Fracture Parameter • Limitations • Ductile-to-Brittle Transition • Impact Fracture Testing • Fatigue • The S-N Curve • Fatigue Strength • Creep

2. Rice’s J-Integral • Parameter which characterizes fracture under elastic-plastic and fully plastic conditions • Similar to the K parameter in fully elastic fracture • Rice defined the J-integral for a cracked body as follows: • W = elastic strain energy density • T = traction vector • u = displacement vector • G = counter clockwise contour beginning on the lower crack surface and ending on any point on the upper crack surface

3. Rice’s J-Integral

4. Rice’s J-Integral • Relation between J and Potential Energy • under linear elastic conditions, J becomes the Griffith’s crack extension force. • Relation is also critical because some derivations of J rely on this concept. • For a body of thickness B:

5. The J-Integral as a Fracture Parameter • JIc and J - Da curves • relationship between J and Da, ductile crack length extension, was hypothesized. • also proposed a physical ductile tearing process during different stages of fracture. • J was only used to specify the onset of ductile tearing, point 3 in the figure. • this point was defined as JIc, the critical J in mode I at the onset of ductile tearing.

6. The J-Integral as a Fracture Parameter • JIc is defined at the intersection of the crack blunting line and the line which defines the J- Da curve. • crack blunting line is described by: • this construction is necessary because it is quite difficult to define this parameter with physical detection to a high degree of consistency.

7. The J-Integral as a Fracture Parameter

8. The J-Integral as a Fracture Parameter • J-dominance • crack tip conditions are equal for all geometries and they are all controlled by the magnitude of J. • large deformation zone (zone of intense deformation) can be expected to extend one CTOD distance beyond the crack tip • this zone is surrounded by a larger zone where J dominance applies. • in order for J to be a valid fracture parameter, all pertinent length parameters (crack size, ligament size, and thickness) all exceed several times dt

9. Example Calculation of the J-Parameter • http://risc.mse.vt.edu/~farkas/cmsms/public_html/jint/cav6.gif • picture not on website!!

10. Limitations of the J-Integral • nonlinear elasticity or deformation theory of plasticity only applies to elastic-plastic materials under monotonic loading • no unloading is permitted • small deformation theory was used in developing: • path independence of J • relationship of J with potential energy, crack tip stress fields and CTOD • stresses cannot exceed 10% or ductility will occur.

11. Ductile-to-Brittle Transition

12. Ductile-to-Brittle Transition • Materials may transition from ductile to brittle behavior • This phenomenon most often occurs in BCC and HCP alloys due to a decrease in temperature. • At low temperatures, materials which experience this transition become brittle. This can lead to rapid, catastrophic failure, with little or no warning.

13. Ductile-to-Brittle Transition • Curve A represents this transition in a steel specimen • The range of temperatures over which this occurs as shown in the next slide is approximately 20 to 80° C

14. Impact Fracture Testing • This temperature range is determined through two standardized testing methods: • Charpy impact testing • Izod impact testing • These tests measure impact energy through the mechanism shown on the next page • The energy expended is computed from the difference between h and h’, giving the impact energy

15. Impact Fracture Testing

16. Impact Fracture Testing

17. Impact Fracture Testing • Energy per unit length crack growth

18. Fatigue • Occurs when a material experiences lengthy periods of cyclic or repeated stresses which can lead to failure at stress levels much lower than the tensile or yield strength of the material. • Fatigue is estimated to be responsible for approximately 90% of all metallic failures • Failure occurs rapidly and without warning. • The stresses acting repeatedly upon the material may be due to • tension-compression type stresses • bending or twisting type stresses

19. Fatigue • The average mean stress, or maximum and minimum stress values are given by: • Stress amplitude is given by: • sr being the range of stress. • And the stress ratio of the maximum and minimum stress amplitudes: • Note that tensile stresses are positive while compressive stresses are always negative

20. The S-N Curve • Data from the tests are plotted as stress S versus the logarithm of the number of cycles to failure, N. • When the curve becomes horizontal, the specimen has reached its fatigue limit • This value is the maximum stress which can be applied over an infinite number of cycles • The fatigue limit for steel is typically 35 to 60% of the tensile strength of the material

21. The S-N Curve • Fatigue testing is performed using a rotating-bending testing apparatus shown below. Figure 8.18. • Specimens are subjected to relatively high cyclic stresses up to about two thirds of the tensile strength of the material. • Fatigue data contains considerable scatter, the S-N curves shown are “best fit” curves.

22. Fatigue Strength • Fatigue strength is a term applied for nonferrous alloys (Al, Cu, Mg) which do not have a fatigue limit. • The fatigue strength is the stress level the material will fail at after a specified number of cycles (e.g. 107 cycles). • In these cases, the S-N curve does not flatten out. • Fatigue lifeNf, is the number of cycles that will cause failure at a constant stress level.

23. Creep • Permanent deformation under a constant stress occurring over time • Three stages of creep: • Primary • Steady-state • tertiary • Testing performed at constant stress and temperature • Deformation is plotted as a function of time

24. Creep