Analytical solutions are derived for interfacial energy release rate and mode mixity angle in the inverted four-point bending test. In the test, the loads applied in the classical four-point bending test are inverted so that the crack faces come into contact at the midspan and mode mixity with an important mode II component is produced. The contact forces are evaluated by employing a beam model and imposing that the two delaminated arms undergo the same deflection at the contact point. Friction is accounted for within an approximate Coulomb model. Both Timoshenko and Euler-Bernoulli beam theories are applied and local 2D effects due to near tip deformations are introduced through suitable analytically derived crack tip root rotations and displacements. The results have been verified by comparison with finite element results. The model accurately estimates energy release rate and mode mixity angle in orthotropic specimens, also for short/intermediate delaminations, and defines the minimum length of the crack ensuring a steady state propagation under a constant value of energy release rate and mode mixity. Steady state propagation under different mode mixity conditions is demonstrated by varying the relative thickness of the delaminated arms.

推导了倒四点弯曲试验中界面能释放速率和模态混合角的解析解。在试验中，将经典的四点弯曲试验中施加的载荷反转，以使裂纹面在中跨处接触，并产生与重要的II型组分的混合模。通过采用梁模型并施加两个分层的臂在接触点处经受相同的挠度来评估接触力。在近似库仑模型中考虑了摩擦。Timoshenko和Euler-Bernoulli梁理论都得到了应用，并且通过适当的分析得出的裂纹尖端根部旋转和位移，引入了由于近尖端变形引起的局部二维效应。通过与有限元结果进行比较来验证结果。该模型还准确估计了正交各向异性标本中的能量释放速率和模式混合角，也适用于短/中间分层，并定义了在能量释放速率和模式混合度恒定的情况下确保稳态传播的最小裂纹长度。通过改变分层臂的相对厚度证明了在不同模式混合条件下的稳态传播。