Reference no: EM132187179
Applied Elasticity and Plasticity Project -
Use a computer program to draw the yield surfaces of the yield criteria given in the table below (a) on deviatoric planes at ρ = 0 and four other different values, where ρ = I1/√3 = √3σm = √3σoct; (b) on meridain planes at θ = 0o, 15o, 30o, 45o, and 60o. (c) Also draw the 3-D perspective views of the yield surfaces in the principal-stress space from three different angles.
|
Yield Criteria
|
Uniaxial Compressive Yield Stress
|
Uniaxial Tensile Yield Stress
|
|
von Mises
|
50,000 psi
|
50,000 psi
|
|
Mohr-Coulomb
|
2,000 psi
|
200 psi
|
|
Yield criterion defined below
|
2,000 psi
|
200 psi
|
The yield surface of the yield criterion is expressed in the form:
F(σ∼) = √3τ0 - r(θ, σ0/σyc, ks) = 0 (1)
where σ∼ is the stress tensor whose Cartesian components are σij, σ0 = I1/3, I1 = σkk = first invariant of stress tensor, τ0 = √(2J2/3), J2 = sijsij/2 = second invariant of the stress deviator sij = σij - 1/3 δijσkk, δij = Kronecker delta, θ = 1/3 cos-1((3√3)/2)J3J2-3/2) = similarity angle which represents the polar angle in the deviatoric section, J3 = 1/3 sijsjkski = third invariant of sij, σyc is the uniaxial compressive yield stress, ks is a constant which determines the size of the yield surface, and function r(θ, σ0/σyc, ks) represents the deviatoric section of the yield surface which can be expressed by the formula
where rt and rc represent the tensile and compression meridians, respectively, which are defined as:
The equations above involve eight parameters α0, · · ·, α3, β0,· · · , β3. These eight parameters and constant ks can be determined based on the following conditions:
1. The two apices of each curve of Eq. 3 and Eq. 4 on the horizontal axis must be common to both curves.
2. The point representing the yield stress under uniaxial tension has to be on the yield surface.
3. The point representing the yield stress under uniaxial compression has to be on the yield surface too.
The above conditions are not enough to determine a unique set of the constant values. Use any set of constants fulfill the above conditions for your project. Include a section in your project report to show the values you use and explain and show calculations how you determine the constants.
Note - It has to be done in Matlab. As for the report of 1000 words need Abstract, intro, procedure, discussion of results, conclusion.
Attachment:- Assignment File.rar