due wednesday june 21 problem 1 elastic thermal strains refer to examp

Question

Due: Wednesday, June 21"
Problem 1: Elastic-Thermal Strains
Refer to example 5.3 (pp. 206-209) and consider the possibility of a temperature change AT in
addition to the stress o₂-75 MPa being applied.
a) For a temperature increase, how would you expect the value of oy to qualitatively change,
as to its magnitude becoming larger or smaller? What happens in the case of a
temperature decrease?
b) Calculate the temperature change that would cause a copper alloy block to be on the
verge of losing contact with the wall in the y-direction.
Given: copper alloy has E= 130 GPa, v=0.343, and a =16.5 x 106 1/°C
Problem 2: Volume Fraction of SiC Fibers
A composite material is to be made by embedding unidirectional SiC fibers in a Ti-alloy metal
matrix. For the composite, the elastic modulus in the fiber direction cannot be less than 250 GPa, and
the shear modulus not less than 60 GPa. What is the minimum volume fraction of fibers is required?
ET = 120 GPa, Esic =396 GPa, V₁.0.361, Vsic = 0.22.
Given:
Problem 3: Elastic Linear-Hardening Model
For the elastic, linear-hardening model of Fig.5.3(c), how is the behavior affected by changing E2
while E₁ remains constant? You may wish to enhance your discussion by including a sketch
showing how the o- path varies with E2.
Problem 4: Elastic-Steady State Creep Model
At 600°C, a silica glass has an elastic modulus E = 60 GPa and a tensile viscosity = 1000 GPa.s.
Assuming elastic-steady state creep behavior, determine the response to a stress of 10 MPa
maintained for 1 minute and then removed. Using Excel, plot &-t for a time interval of 2 minutes
(use increment of 10 seconds).
Problem 5: Relaxation Model
Consider relaxation under constant strain & of a model with spring and dashpot in series, as in
Fig.5.6, but let the dashpot behave according to the nonlinear equation:
k=Ba"
where B and m are material constants, with m being typically in the range of 3 to 7. Derive an
equation for o as a function of e', time t, and the various model constants.
Need handwritten solution for all questions