Slip in Single Crystals 2. Consider a metal single crystal oriented such that the normal to the slip plane and the slip direction are at angles of $ and λ, respectively, with the tensile axis. If the critical resolved shear stress is TCRSS, will an applied stress of σ cause the single crystal to yield? If not, what stress will be necessary? = Use 43.1°; λ = 47.9° %; TCRSS = 20.7 MPa ; σ = 45 MPa

Consider a metal single crystal oriented such that the normal to the slip plane and the slip direction are at angles of 43.1° and 47.9°, respectively, with the tensile axis. If the critical resolved shear stress is 20.7 MPa (3000 psi), will an applied stress of 45 MPa (6500 psi) cause the single crystal to yield? If not, what stress will be necessary?

2. Another cylindrical component is madeof Enfennering ceramic Al203 but with different dimensions. Here, l=30 cm and the diameter is 4 cm. Assume the same Weibull modulus of 9. Calculate the level of the tensile strength for the following probability of failures: a. Pr (V) = 0.1 b. Pr (Vo) = 0.01 c. What is the survival probability and the failure probability of this component if a stress of 200 MPa is applied?

The diagram below shows a microscopic metal rod with a single crystal structure whose orientation is indicated by the inset. A force of F = 14.9 N is applied to the rod. The cross-sectional area is 1.1 mm². Calculate the shear stress along the close-packed direction. Dogo ooooo a. 4.65 MPa O b. 6.08 MPa c. 5.09 MPa O d. 4.04 MPa O e. 5.53 MPa

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What is the maximum value of KIc as per LEFM that can be determined from experiments on a 20 mm thick plate? yield strength= 500 MPa, E= 210 GPa, poission ratio=0.3.

QUESTION 2 (a) Stress and strain diagram of 316L stainless steel is plotted in Figure Q2 (a). Determine and label the following terms: (i) Proportional limit point (0,ɛ) (ii) Yield point (0,ɛ) (iii) Ultimate point (0,8) (iv) Fracture point (0,8) (iv) Modulus of elasticity or Young's modulus (E) 700 400 600 500 300 400 200 6 300 200 E 100 100 0.005 0.01 0.015 0.02 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Strain, E (mm/mm) Strain, E (mm/mm) Figure Q2 (a) (b) A short post AB constructed from a hollow circular tube of aluminium, supports a compressive load of 116 kN as in Figure Q2 (b). The inner and outer diameters of the tube are di=100 mm and dz=112 mm, respectively, and its length is 400 mm. The shortening of the post due to the load is measured as 0.3 mm. Determine the compressive stress and strain in the post. Note: the weight of the post is neglected. 116 KN A 400 mm Figure Q2 (b) Stress, o (MPa) Stress, a (MPa)

Determine the critical resolved shear stress on a BCC single crystal if a normal stress of 10 MPa along [100] direction causes slip system on (110) plan along [1-11], one-bar one-one, direction.

Consider an iron single crystal with CCC crystal structure oriented in such a way that a tensile stress is applied to the along one direction [010]. a) Calculate the shear stress resolved along a plane (110) and a direction when a tensile stress of 52 MPa is applied. The normal to the slip plane forms 45° with traction direction. the direction of slip forms 55º with the traction direction. b) If the slip occurs in one plane (110) and in one direction and the critical resolved shear stress is 30 MPa, calculate the magnitude of tensile stress that must be applied to initiate the flow.