(Solved): A rod is undergoing tensile testing. A neck develops along the gage length of the rod prior to fail ...

A rod is undergoing tensile testing. A neck develops along the gage length of the rod prior to failure as shown in Figure Qn A2(a). Figure un A<(a) Describe the Bridgman correction in the context of the rod. Illustrate your answer with a sketch for full marks. (5 marks) (b) Bulge testing is widely used in industry to study mechanical performance of materials in sheet form. It is widely used to determine stress $?$ of materials at large strains. (i) Sketch a schematic of a cross-section of a specimen undergoing a bulge test. ( 3 marks) (ii) Use the sketch in part (i) immediately above to derive the relationship for stress, $?$ during bulge test: $?=\frac{P?}{2t}$ State your workings clearly for full marks. (7 marks) (c) Anisotropy in sheet materials need to be characterised to ensure manufacturing processes are repeatable and consistent. (i) What is sheet anisotropy? (3 marks) (ii) Describe with as much detail as possible, how you would determine anisotropy in sheet materials. (7 marks) (a) Fatigue refers to the failure of materials when exposed to cyclic loading. Some materials exhibit an endurance limit. (i) State the three requirements for fatigue to take place. (3 marks) (ii) Sketch an S-N curve for a material with and without an endurance limit. Label the curves accordingly. (4 marks) (iii) A component is polished until its surface is very smooth. However, after it is exposed to cyclic load, fatigue cracks were observed on the surface. Explain how the cracks could be formed. ( 3 marks) (b) Stress amplitude $S$ versus number of cycles to fatigue failure $\mathrm{N}$ of three alloys are shown in Figure Qn B1(b). (i) An $8.0\mathrm{mm}$ diameter cylindrical rod fabricated from a red brass alloy in Figure Qn B1(b) is subjected to reversed tension-compression load cycling along its axis. If the maximum tensile and compressive loads are $7500\mathrm{N}$ and $?7500\mathrm{N}$ respectively, determine its fatigue life. (5 marks) (ii) Suppose that the fatigue data for the 1045 steel were taken from torsional tests, and that a shaft of this alloy is to be used for a coupling that is attached to an electric motor operating at $1500\mathrm{rpm}$. Give the maximum torsional stress amplitude possible for the coupling to have a life-time of at least 1 year. ( 5 marks) Section A: Answer ALL questions. an A1 (a) The stress state of an element on the surface of a shaft is shown in Figure Qn 1(a): r?gure un $4\pm [a]$ (i) Draw the Mohr's circle on a graph paper. Indicate points A and B, coordinates of center point and radius of circle. Label the horizontal and vertical axes. (7 marks) (ii) Determine the principal stresses ( 2 marks) (iii) Determine the maximum shear stress (1 marks) (iv) Use the method of stress tensor to determine the: - principal stresses (2 marks) - angle $?$ (5 marks) (b) A thin composite sheet is to be made from fibres that are aligned in the $x$-direction as shown in Figure Qn A1(b). The material is anisotropic with Young's modulus of $E_x=$ $150\mathrm{GPa}$ and $E_y=5\mathrm{GPa}$ in the $x$ and $y$ directions, respectively. The sheet is subjected to ${?}_x,{?}_y,{?}_{yx}$ and ${?}_{xy}$ only. The Poisson ratio of the material is $v$. Strain and stress components can be related by the reduced compliance matrix as below. $?\begin{array}{c}{?}_x\\ {?}_y\\ {?}_{xy}\end{array}?=?\begin{array}{lll}{s}_{11}& s_{12}& s_{13}\\ s_{21}& s_{22}& s_{23}\\ s_{31}& s_{32}& s_{33}\end{array}??\begin{array}{c}{?}_x\\ {?}_y\\ {?}_{xy}\end{array}?$ The in-plane shear modulus of the composite sheet is $G_{xy}=7.5\mathrm{GPa}$ and its Poisson ratio is $v=0.25$. The thin composite sheet is subjected to plane stress such that $?\begin{array}{c}{?}_x\\ {?}_y\\ {?}_{xy}\end{array}?=?\begin{array}{c}0.50\\ 0.50\\ 0.50\end{array}?$ GPa. Determine the strain matrix $?\begin{array}{c}{?}_x\\ {?}_y\\ {?}_{xy}\end{array}?$ of the sheet. Show your workings clearly. (10 marks)