A piece of BCC single-crystal metal is oriented such that tensile stress is applied along a [131] direction. If slip occurs on a (011) plane and in a [111] direction, compute the stress at which the crystal yields if its critical resolved shear stress is 12 MPa.

A large plate is fabricated from a steel alloy that has a plane strain fracture toughness of 55 MPa√m. If during service use, the plate is exposed to a tensile stress of 200 MPa, compute the minimum length of a surface crack that will lead to a fracture. Assume the value of 1.0 for Y.

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1. For the stress-strain curve shown below, please estimate the properties indicated. (a) Fracture Strain Please do your work on a separate sheet of paper, and put your answers in the boxes on the right. Be sure to include the proper symbol and units. Stress Strain 70 60 50 Stress (ksi) 240 30 20 10 70 0 0.000 60 50 Stress (ksi) 40 20 10 KULL 0 0.000 0.010 0.050 0.100 Strain (in/in) Stress Strain 0.020 0.030 Strain (in/in) 0.040 0.150 0.050 (b) Ultimate Tensile Stress (c) Fracture Stress (d) Proportional Limit (e) Elastic Modulus (1) Yield Stress (g) Tensile Toughness (Modulus of Toughness) (h) Modulus of Resilience

(a) An AISI steel plate has width W = 30 cm and a central crack with size of 3 mm. The plate is under a uniform stress. Find the maximum value of the stress is KIc = 50 MPa m1/2. (b) If the part has to operate at a stress of 1,500 MPa, compute the maximum crack size that the plate can have.

5. How much more or less likely is it for a brittle material with volume V to fail compared to the same material with volume Vo/2 at the same applied stress? Why is this the case? Talk specifically in the context of flaw landscape.

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6.27 Compute the dislocation density in tungsten if the flow stress is controlled by the stress necessary to operate a Frank--Read source. The shearstress in the slip plane is 50 MPa. Take G = 166 GPa.

(a) An AISI 4340 steel plate has a width W of 30 cm and has a central crack 2a of 3 mm. The plate is under a uniform stress σ. This steel has a KIc value of 50 MPa m1/2. Find the maximum stress for this crack length. (b) If the operating stress is 1,500 MPa, compute the maximum crack size that the steel may have without failure

A component made of 7075-T6 aluminum alloy has an edge crack of 1.4 mm in length. Plane strain fracture toughness of this alloy is given as 27 MPavm. Geometrical factor of the crack is given as 1.2. (a) If this alloy is subjected to uniaxial tensile stress of 380 MPa, determine whether sudden brittle fracture occurs or not. (b) Calculate the maximum allowable crack size for this component in order not to be failed in brittle manner under a stress of 1000 MPa (Density of steel 7.85 g/cm³, 9.80665 N = 1 kg). Modulus of elastisity, GPa Ultimate tensile Yield strength, Alloy strength, MPa MPa 2014 Al alloy Bronze (92Cu-8Sn) High carbon steel Pure Titanium 97 186 380 72 110 152 380 615 215 240 330 107