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   "source": [
    "# Chapter 4: Plastic Deformation of Single Crystals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 4.1, Critical Resolved Shear Stress for Slip, Page No. 125"
   ]
  },
  {
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   "execution_count": 4,
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tensile Stress applied = 14.6969 MPa\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "import numpy as np\n",
    "\n",
    "#variable declaration\n",
    "a=[1,-1,0];\n",
    "n=[1,-1,-1];\n",
    "s=[0,-1,-1];\n",
    "Tr=6;\n",
    "\n",
    "#calculation\n",
    "cos_fi=np.dot(a,n)/(sqrt(a[0]**2+a[1]**2+a[2]**2)*sqrt(n[0]**2+n[1]**2+n[2]**2));\n",
    "cos_lm=np.dot(a,s)/(sqrt(a[0]**2+a[1]**2+a[2]**2)*sqrt(s[0]**2+s[1]**2+s[2]**2));\n",
    "sigma=Tr/(cos_fi*cos_lm);\n",
    "\n",
    "#result\n",
    "print('Tensile Stress applied = %g MPa')%(sigma);"
   ]
  },
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   "execution_count": null,
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