(32 points) You are going to be evaluating the properties of PEEK with new additives to increase its fracture toughness. The baseline expected properties of PEEK are: Yield strength of 85 MPa, ultimate tensile strength of 95 MPa, elongation to failure of 50%, fracture toughness of 3.4 MPa//m, Young's Modulus 3.8 GPa, and Poisson's ratio 0.38, (a) What is the materials critical strain energy release rate? (b) Write out the relationship between the stress intensity factor and the applied load. (c) What are the minimum dimensions b, a and h that are allowed for this to be an valid test of the fracture toughness assuming you do not actually increase the fracture toughness? (d) If you estimate that the fracture toughness will increase by 20% and the yield strength decreases by 15%, what percent will you need to increase your dimensions for a valid test? (e) Assuming a = 2.5 cm, b=2.5 cm, L=20.0 cm, h=1.0 cm, what is the load you would expect fast fracture at? (f) If increase the fracture toughness with your additives, how would your additives affect the ductility, Young's modulus and glass transition temperature of PEEK? Explain. The stress intensity factor is: P O G = 12Pa Ebh 2h