Plot the singular stress components sigmaxx sigmayy and

Question

Question 1 -

1) Plot the singular stress components, σ_xx, σ_yy and τ_xy for a cracked body under Mode I, Mode II and Mode III loading with a stress intensity factor K_i = 10 MPa·m^1/2 (i = I, II and III). Plot the stresses near the crack tip (r < 2 mm). In order to obtain a meaningful figure, take into account that the stresses for very short r tend to infinity (singularity). It is recommended to use Matlab (file guide_plot2D.m may provide some guidelines).

2) Consider the Mode I case. Assume that the material exhibits a yield stress of 150 MPa. Make use of the Von Misses yield criteria to plot the contour of the zone near the crack tip were the material is expected to yield. Answer this question for

i) Plane stress

ii) Plane strain

Compare both results in the same plot. Again, it is recommended to use Matlab (file guide_contour2D.m may provide some guidelines). The Von Misses stress criteria in local coordinates reads:

σ_y = (1/√2)√((σ_x-σ_y)² + (σ_y-σ_z)² + (σ_z-σ_x)² + 6(τ_xy²+τ_yz²+τ_zx²))

Assume that the Poisson ratio, ν, is 0.3

Question 2 -

A metallic plate under an uniaxial remote load, has an inclined crack, which is small compared with the dimensions of the plate.

Plot the critical load vs. the inclination angle (β).

Geometry of the plate:

W = 400 mm

B = 13 mm

2a = 30 mm

Material properties:

σ_ys = 320 MPa

K_IC = 22 MPa·m^½

Plot inclination angle (β) from 0 to 90 every 5 degree.

Need it as per the guidelines

Attachment:- Assignment Detail.rar