Statistical fracture modeling: crack path and fracture criteria with application to homogeneous and functionally graded materials

摘要: Abstract Analysis has been performed on fracture initiation near a crack in brittle material with strength described by Weibull statistics. This nonlocal model allows for direct correlation between crack-tip stresses and failure. Predictions are made both the toughness average angle of under mixed-mode loading. is pertinent composites especially interesting functionally graded materials (FGMs), where stress fields vary from homogeneous form away tip. Both analytic finite element analyses FGMs reveal that gradients scaling σ 0 ( x , y ) usually lead to dramatic decrease toughness; moreover, normal result growing toward weaker material. When comparing Young's modulus direction path, E ), same stress-intensity factor K into steeper negative gradient will be tougher, if m modulus, low; growth stiff direction, effect opposite. These effects offset higher-stress intensity cracks more compliant material, shielding when stiffer based upon expectations applied load. Perpendicular can cause far-field mode I loading produce tip other asymmetric adjustments field; induces non-coplanar cracking depends strongly . The distribution damage For high materials, failure dominated very near-tip parameters, minimized. With low distributed leading toughening exaggerated FGMs. Finally, consideration given role several higher-order terms field.