Correct the angle theta for crack extension direction and check for m…

…aximum sigma refs idaholab#29921
tranm-ansto · Feb 24, 2025 · b4bf806 · b4bf806
1 parent 7763735
commit b4bf806
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Showing 7 changed files with 34 additions and 11 deletions.
diff --git a/modules/xfem/src/userobjects/MeshCut2DFractureUserObject.C b/modules/xfem/src/userobjects/MeshCut2DFractureUserObject.C
@@ -149,12 +149,35 @@ MeshCut2DFractureUserObject::findActiveBoundaryGrowth()
       Real k_squared = _ki_vpp->at(i) * _ki_vpp->at(i) + _kii_vpp->at(i) * _kii_vpp->at(i);
       if (k_squared > (k_crit * k_crit) && _ki_vpp->at(i) > 0)
       {
-        // growth direction in crack front coord (cfc) system based on the  max hoop stress
-        // criterion
+        // growth direction in crack front coord (cfc) system based on the max hoop stress criterion
+        // Ref "Ceramic nuclear fuel fracture modeling with the extended finite element method" by
+        // W. Jiang, B. Spencer, and J. Dolbow
+        // Equation 6
         Real ki = _ki_vpp->at(i);
         Real kii = _kii_vpp->at(i);
-        Real sqrt_k = std::sqrt(ki * ki + kii * kii);
-        Real theta = 2 * std::atan((ki - sqrt_k) / (4 * kii));
+        Real sqrt_k = std::sqrt(ki * ki + 8 * kii * kii);
+        theta_m = 2 * std::atan((ki - sqrt_k) / (4 * kii));
+        theta_p = 2 * std::atan((ki + sqrt_k) / (4 * kii));
+
+        // check sigma_tt
+        // Ref "Ceramic nuclear fuel fracture modeling with the extended finite element method" by
+        // W. Jiang, B. Spencer, and J. Dolbow
+        // Equation 5
+        const Real & r = _growth_increment;
+        Real sigma_tt_m = (ki / (4 * std::sqrt(2 * M_PI * r))) *
+                              (3 * std::cos(theta_m / 2) + std::cos(3 * theta_m / 2)) +
+                          (kii / (4 * std::sqrt(2 * M_PI * r))) *
+                              (-3 * std::sin(theta_m / 2) - 3 * std::sin(3 * theta_m / 2));
+        Real sigma_tt_p = (ki / (4 * std::sqrt(2 * M_PI * r))) *
+                              (3 * std::cos(theta_p / 2) + std::cos(3 * theta_p / 2)) +
+                          (kii / (4 * std::sqrt(2 * M_PI * r))) *
+                              (-3 * std::sin(theta_p / 2) - 3 * std::sin(3 * theta_p / 2));
+        Real theta;
+        if (sigma_tt_m > sigma_tt_p)
+          theta = theta_m;
+        else
+          theta = theta_p;
+
         RealVectorValue dir_cfc;
         dir_cfc(0) = std::cos(theta);
         dir_cfc(1) = std::sin(theta);

diff --git a/modules/xfem/test/tests/mesh_cut_2D_fracture/edge_crack_2d_propagation.i b/modules/xfem/test/tests/mesh_cut_2D_fracture/edge_crack_2d_propagation.i
@@ -59,7 +59,7 @@
 [Functions]
   [pull_func]
     type = ParsedFunction
-    expression = 0.00025*(1+t)
+    expression = 0.000307*(1+t)
   []
 []
 

diff --git a/...sts/mesh_cut_2D_fracture/gold/kcrit_based_meshCut_uo_xfemcutter_XFEMCutMeshOutput.e-s0004 b/...sts/mesh_cut_2D_fracture/gold/kcrit_based_meshCut_uo_xfemcutter_XFEMCutMeshOutput.e-s0004
diff --git a/...h_cut_2D_fracture/gold/kcrit_stress_based_meshCut_uo_xfemcutter_XFEMCutMeshOutput.e-s0004 b/...h_cut_2D_fracture/gold/kcrit_stress_based_meshCut_uo_xfemcutter_XFEMCutMeshOutput.e-s0004
diff --git a/...ests/mesh_cut_2D_fracture/gold/kvpp_based_meshCut_uo_xfemcutter_XFEMCutMeshOutput.e-s0004 b/...ests/mesh_cut_2D_fracture/gold/kvpp_based_meshCut_uo_xfemcutter_XFEMCutMeshOutput.e-s0004
diff --git a/...ts/mesh_cut_2D_fracture/gold/stress_based_meshCut_uo_xfemcutter_XFEMCutMeshOutput.e-s0004 b/...ts/mesh_cut_2D_fracture/gold/stress_based_meshCut_uo_xfemcutter_XFEMCutMeshOutput.e-s0004
diff --git a/modules/xfem/test/tests/nucleation_uo/gold/nucleate_edge_bulk_crack_2d_out_II_KI_1_0011.csv b/modules/xfem/test/tests/nucleation_uo/gold/nucleate_edge_bulk_crack_2d_out_II_KI_1_0011.csv
@@ -1,7 +1,7 @@
 II_KI_1,id,x,y,z
-179.96644885549,0,-1.7959413469933,0.60067940319072,0
-109.79588615536,0,-0.08927463374154,0.56672807537366,0
-117.47541725669,0,0.10286914470109,0.62758078178023,0
-121.35976891745,0,1.9086197693201,0.59850479007701,0
-162.95197012485,0,-2.3641336046242,0.56270032134112,0
-161.30835857761,0,2.3644735531981,0.56381094263482,0
+223.68734442443,0,-1.6630008798218,0.65061751080966,0
+195.08900551755,0,-0.23539145914144,0.67909757143352,0
+185.58601592247,0,0.24487407919304,0.69909531689729,0
+158.69110493045,0,1.7711042455497,0.68594035263257,0
+182.95885629805,0,-2.4358688580963,0.7050913486118,0
+184.08215627613,0,2.4363905397662,0.70540653100326,0