用于拉伸主导型脆性断裂相场建模的移位能垒方法
A shifted energy barrier approach for phase-field modeling of tensile-dominated brittle fracture
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中文总结 AI 辅助
本文提出一种移位能垒方法，改进经典AT1相场模型，实现拉伸主导型脆性断裂的精准建模，可复现峰值强度、捕捉形核规律及失效模式转变，且形核载荷对正则化长度不敏感。
中文摘要 AI 辅助
经典AT1相场模型包含裂纹形核的固有能量垒，这使得预测强度依赖于断裂韧性和正则化长度。针对拉伸主导型脆性断裂，本文通过将基于有效应力评估的Rankine准则映射到与状态相关的主动能阈值，实现该能垒的移位。此时规定的拉伸强度控制裂纹形核，而AT1的裂纹密度泛函、刚度退化及退化应力响应保持不变。由于阈值依赖于当前应力状态，场方程由受限变分原理推导得到。微力公式将该能垒移位识别为耗散阻力，并给出正则化长度的对应下界。在一维拉伸情形下，闭式解可复现规定的峰值强度，并给出余弦型局域化轮廓，当移位消失时该轮廓趋近于经典AT1轮廓。数值算例表明，在可容许范围内，形核载荷对正则化长度几乎不敏感，且预测的多轴形核状态符合Rankine包络；在整体压缩下，裂纹形核仍与局部拉应力集中相关，该公式还能捕捉从小缺陷的强度控制失效到大裂纹的线弹性断裂力学（LEFM）极限的转变过程。
英文摘要
The classical AT1 phase-field model contains an intrinsic energy barrier for crack nucle ation, which makes the predicted strength depend on the fracture toughness and the regularization length. For tensile-dominated brittle fracture, this barrier is shifted by mapping the Rankine criterion, evaluated on the effective stress, onto a state-dependent active-energy threshold. The prescribed tensile strength then controls crack nucleation, while the AT1 crack-density functional, stiffness degradation, and degraded stress response remain unchanged. Since the threshold depends on the current stress state, the field equations are derived from a restricted variational principle. A microforce formulation identifies the barrier shift as a dissipative resistance and provides the corresponding lower bound on the regularization length. In one-dimensional tension, closed-form solutions recover the prescribed peak strength and give a cosine-type localization profile that ap proaches the classical AT1 profile as the shift vanishes. Numerical examples show that, within the admissible range, the nucleation load is nearly insensitive to the regularization length and the predicted multiaxial nucleation states follow the Rankine envelope. Under overall compression, crack nucleation remains associated with local tensile stress concen trations. The formulation also captures the transition from strength-controlled failure for small flaws to the LEFM limit for large cracks.
