5. The resistance curve

The resistance curve of a material fits the expression

Regard Ko, Kss and Lss as material parameters. The material has crack like flaws of length

2a. When the material is under stress o, the cracks may grow stably to size 2a and

assume that the stress intensity factor is given by:

(a) Sketch this curve and explain the meanings of the parameters Ko, Kss, and Lss.

(b) Describe a procedure to determine the maximum stress, o*, which the material can carry without breaking and the stable crack extension, Aa* before the material breaks under the maximum stress.

(c) A material has Ko = 1 MPa√m, Kss = 10 MPa√m, and Lss = 10 µm. Plot the strength as a function of the flaw size in the range a,-5-50 µm. Make a similar plot for a material having Lss=20μm. Discuss the effect of increasing Lss.

(d) Plot your results in a dimensionless form. For example, plot o*√√Lss/Ko as a function of a/Lss, at several levels of Kss/Ko. Discuss the implications of increasing the initial flaw size or Kss/Ko.

(e) Plot Aa*/ Lss as a function of a/Lss, at several levels of Kss/Ko, discuss the plot.