Question

2. A 1-meter long cylindrical rod made of near-perfect metal has an elastic modulus of 50 GPa and yield strength of 50 MPa. The rod is anticipated to sustain up to a tensile force of 1 x 10°N in an engineering application. (a) If only 1 mm of elongation is allowed, what is the minimum diameter for the rod? [15 points) (b) The yield strength of the rod is too small for certain applications. Smaller grains need to be created to increase the yield strength. It is known that the yield strength is 150 MPa under an average grain size of 0.0625 mm. What average grain size will lead to a yield strength of 300 MPa? [20 points)

Answer 1

2a) Civen Length of cylindrical rod- i -L modelus of elasticity - 50 G Pa Axial force acting – 1x10N -P allowed & elongation = 15m.com AL To find minimum diameter for the rod doin Use the relation on AL- PL EA P- Force acting t o dote (- length E modulus of elastility A Cross sectional area A=I d2 were dis diameter a . foto . APL - E. TT d² 0.001 - tox Soxio 2 0.00254 1084 d. c 50x10° X 4 X 0.001 m d- 0.05

Minimum diameter of rod to sustain 100N ON colthy is 5cm. 1mm elongation 6) Given by = 150 MPa d, - o. 0625 mm. cy, - 300 MPa To find grain size to get yield strength 300 mpa calculations Hall- Petch relation Gy - Go + Kylo lolote va by - yield stress 6 > material constant . (starting stress.) ky strengthening coefficierst (material consta a grain size Here only one. Set of value for by and d oven. So we cannot use the relation. an answer. We can. Approxima Gya

de- disse de 0.0625 () - 0.0625 0.0 15.625 mm.
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