TMM4175 Polymer Composites

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Comparing failure criteria¶

Previously implemented functions:

from compositelib import fE_maxstress, fE_maxstrain, fE_tsaiwu, fE_hashin

Material properties for the examples:

import matlib
m1=matlib.get('Carbon/Epoxy(a)')

import matplotlib.pyplot as plt
%matplotlib inline
fig,ax = plt.subplots(figsize=(8,4))
# empty list of normal stresses in the 1-2 plane:
s1_MS,s2_MS=[],[]  # maximum stress
s1_ME,s2_ME=[],[]  # maximum strain
s1_TW,s2_TW=[],[]  # tsai-wu

from math import cos,sin,radians
for a in range(0,3600):
    s1i=cos(radians(a/10))
    s2i=sin(radians(a/10))
    feMS=fE_maxstress((s1i,s2i,0,0,0,0),m1)
    feME=fE_maxstrain((s1i,s2i,0,0,0,0),m1)
    feTW=fE_tsaiwu((s1i,s2i,0,0,0,0),m1)
    # then scaling by the load-proportionality ratio (1/fE):
    s1_MS.append(s1i/feMS)
    s2_MS.append(s2i/feMS)
    s1_ME.append(s1i/feME)
    s2_ME.append(s2i/feME)
    s1_TW.append(s1i/feTW)
    s2_TW.append(s2i/feTW)
    
ax.plot(s1_MS,s2_MS,'--',color='black',label='Max Stress',linewidth=1)
ax.plot(s1_ME,s2_ME,'--',color='blue',label='Max Strain',linewidth=1)
ax.plot(s1_TW,s2_TW,'--',color='green',label='Tsai-Wu',linewidth=1)

ax.plot((0,),(0,),'+',color='black',markersize=50)
ax.grid(True)
ax.legend(loc='best')

ax.set_xlabel(r'$\sigma_1$',fontsize=14)
ax.set_ylabel(r'$\sigma_2$',fontsize=14)

plt.tight_layout()

import matplotlib.pyplot as plt
%matplotlib inline
fig,ax = plt.subplots(figsize=(6,6))
s2_MS,s3_MS=[],[]
s2_ME,s3_ME=[],[]
s2_TW,s3_TW=[],[]
s2_HH,s3_HH=[],[]
from math import cos,sin,radians
for a in range(0,3600):
    s2i=cos(radians(a/10))
    s3i=sin(radians(a/10))
    feMS=fE_maxstress((0,s2i,s3i,0,0,0),m1)
    feME=fE_maxstrain((0,s2i,s3i,0,0,0),m1)
    feTW=fE_tsaiwu((0,s2i,s3i,0,0,0),m1)
    feHH=fE_hashin((0,s2i,s3i,0,0,0),m1)[1]
    # then scaling by the load-proportionality ratio (1/fE):
    s2_MS.append(s2i/feMS)
    s3_MS.append(s3i/feMS)
    s2_ME.append(s2i/feME)
    s3_ME.append(s3i/feME)
    s2_TW.append(s2i/feTW)
    s3_TW.append(s3i/feTW)
    if feHH>0:
        s2_HH.append(s2i/feHH)
        s3_HH.append(s3i/feHH)
    
ax.plot(s2_MS,s3_MS,'--',color='black',label='Max Stress',linewidth=1)
ax.plot(s2_ME,s3_ME,'--',color='blue',label='Max Strain',linewidth=1)
ax.plot(s2_TW,s3_TW,'--',color='green',label='Tsai-Wu',linewidth=1)
ax.plot(s2_HH,s3_HH,'--',color='orange',label='Hashin',linewidth=1)

ax.plot((0,),(0,),'+',color='black',markersize=50)
ax.grid(True)
ax.legend(loc='best')

ax.set_xlabel(r'$\sigma_2$',fontsize=14)
ax.set_ylabel(r'$\sigma_3$',fontsize=14)

ax.set_xlim(-300,100)
ax.set_ylim(-300,100)

plt.tight_layout()

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