diff --git a/Calc_kappa.py b/Calc_kappa.py
index 55f88ed..ee5f3c8 100644
--- a/Calc_kappa.py
+++ b/Calc_kappa.py
@@ -106,7 +106,11 @@ def integrationSigmaX(k):
 def f(k, ans):
     return integrationSigmaX(k)/integrationSigmaZ(k) - ans
 
-ans = 17.53667954
+sigma_x = 0.0038610038610 # conductivty (S/m) along x-axis
+sigma_z = 0.0002201673272 # conductivty (S/m) along z-axis
+sigma_l = 21.0 # conductivity (S/m) of the coductive phase in cracks
+
+ans = sigma_x / sigma_z
 eps = 0.001
 a = -10.0
 b = 10.0
@@ -118,11 +122,10 @@ def f(k, ans):
     else:
         a = c
     if abs(f(c, ans)) < eps:
-        fileName = 'kappa.txt'
+        fileName = 'kappa_phi.txt'
         f = open(fileName, 'w')
         f.write("kappa: " + str(c) + "\n")
-        f.write("factor X: " + str(integrationSigmaX(c)) + "\n")
-        f.write("factor Z: " + str(integrationSigmaZ(c)) + "\n")
+        f.write("crack volume fraction: " + str(sigma_z/integrationSigmaZ(c)/sigma_l) + "\n")
         f.close()
         break
     n += 1
diff --git a/CrackX.py b/CrackX.py
index b8c200d..94084b0 100644
--- a/CrackX.py
+++ b/CrackX.py
@@ -75,12 +75,15 @@ def integration(k):
         result += 0.5 * dTheta * (sum1 + sum2)
     return result
 
-fileName = 'crack_x.csv'
+phi=0.01 #volume fraction (0 <= phi <= 1.0)
+sigma_l = 1.0 # conductivity (S/m) of the coductive phase in cracks
+fileName = 'crack_sigma_x.csv'
 f = open(fileName, 'w')
+f.write("kappa, sigma_x"+'\n')
 list = (100.0, 50.0, 30.0, 20.0, 10.0, 5.0, 3.0, 2.0, 1.0, 0.0, -1.0, -2.0, -3.0, -5.0, -10.0, -20.0, -30.0, -50.0, -100.0)
-for k in list:
-    result = integration(k)
-    s = str(k)+','+str(result)+'\n'
+for kappa in list:
+    sigma_x = integration(kappa) * sigma_l * phi # conductivity (S/m)
+    s = str(kappa)+','+str(sigma_x)+'\n'
     f.write(s)
     f.flush()
 f.close()
diff --git a/CrackZ.py b/CrackZ.py
index 52b13e5..89bba85 100644
--- a/CrackZ.py
+++ b/CrackZ.py
@@ -72,12 +72,15 @@ def integration(k):
         result += 0.5 * dTheta * (sum1 + sum2)
     return result
 
-fileName = 'crack_z.csv'
+phi=0.01 #volume fraction (0 <= phi <= 1.0)
+sigma_l = 1.0 # conductivity (S/m) of the coductive phase in cracks
+fileName = 'crack_sigma_z.csv'
 f = open(fileName, 'w')
+f.write("kappa, sigma_z"+'\n')
 list = (100.0, 50.0, 30.0, 20.0, 10.0, 5.0, 3.0, 2.0, 1.0, 0.0, -1.0, -2.0, -3.0, -5.0, -10.0, -20.0, -30.0, -50.0, -100.0)
-for k in list:
-    result = integration(k)
-    s = str(k)+','+str(result)+'\n'
+for kappa in list:
+    sigma_z = integration(kappa) * sigma_l * phi # conductivity (S/m)
+    s = str(kappa)+','+str(sigma_z)+'\n'
     f.write(s)
     f.flush()
 f.close()
diff --git a/TubeX.py b/TubeX.py
index 46cb0c3..6b7dda7 100644
--- a/TubeX.py
+++ b/TubeX.py
@@ -75,12 +75,15 @@ def integration(k):
         result += 0.5 * dTheta * (sum1 + sum2)
     return result
 
-fileName = 'tube_x.csv'
+phi=0.01 #volume fraction (0 <= phi <= 1.0)
+sigma_l = 1.0 # conductivity (S/m) of the coductive phase in cracks
+fileName = 'tube_sigma_x.csv'
 f = open(fileName, 'w')
+f.write("kappa, sigma_x"+'\n')
 list = (100.0, 50.0, 30.0, 20.0, 10.0, 5.0, 3.0, 2.0, 1.0, 0.0, -1.0, -2.0, -3.0, -5.0, -10.0, -20.0, -30.0, -50.0, -100.0)
-for k in list:
-    result = integration(k)
-    s = str(k)+','+str(result)+'\n'
+for kappa in list:
+    sigma_x = integration(kappa) * sigma_l * phi # conductivity (S/m)
+    s = str(kappa)+','+str(sigma_x)+'\n'
     f.write(s)
     f.flush()
 f.close()
diff --git a/TubeZ.py b/TubeZ.py
index 4cd2afb..dd51beb 100644
--- a/TubeZ.py
+++ b/TubeZ.py
@@ -72,12 +72,15 @@ def integration(k):
         result += 0.5 * dTheta * (sum1 + sum2)
     return result
 
-fileName = 'tube_zx.csv'
+phi=0.01 #volume fraction (0 <= phi <= 1.0)
+sigma_l = 1.0 # conductivity (S/m) of the coductive phase in cracks
+fileName = 'tube_sigma_z.csv'
 f = open(fileName, 'w')
+f.write("kappa, sigma_z"+'\n')
 list = (100.0, 50.0, 30.0, 20.0, 10.0, 5.0, 3.0, 2.0, 1.0, 0.0, -1.0, -2.0, -3.0, -5.0, -10.0, -20.0, -30.0, -50.0, -100.0)
-for k in list:
-    result = integration(k)
-    s = str(k)+','+str(result)+'\n'
+for kappa in list:
+    sigma_z = integration(kappa) * sigma_l * phi # conductivity (S/m)
+    s = str(kappa)+','+str(sigma_z)+'\n'
     f.write(s)
     f.flush()
 f.close()