Background: Identification of damage at an early stage is crucial for critical structural components. Objective: Creep induced micro-voids in heat treated polycrystalline pure copper are experimentally and numerically characterized. Methods: This is accomplished by the use of non-linear ultrasonic waves. Numerically, the study is carried out on an elastic material with randomly located micro-voids. The finite difference in time domain method is used. Results: Experimentally it is found that material damage due to micro-voids that are developed before 40% creep life may effectively be detected with nonlinear ultrasonic waves in the low power regime. Increase in second order nonlinearity parameter with percentage creep life is observed along with the corresponding increase in micro-void concentration. Optical metallography and micro-hardness measurements were used to corroborate the experimental results. For the numerical studies, void dimensions selected for study are much lower than the probing wave length. Concentration of micro-voids is varied from 0.01% to 3%. The second order nonlinearity parameter showed a slight increase in the initial stages and an abrupt increase with higher micro-void concentration in simulations. This agrees with experimental trends. Conclusion: The feasibility of detecting micro-voids in the early stages of creep using nonlinear ultrasonic waves is experimentally demonstrated and a simple model with voids is numerically studied to show the sensitivity of the second order nonlinearity parameter to micro voids.

中文翻译：

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蠕变引起的微孔洞产生二次谐波的实验和数值研究

背景：在早期阶段识别损坏对于关键结构部件至关重要。目的：通过实验和数值表征热处理多晶纯铜中蠕变诱发的微孔洞。方法：这是通过使用非线性超声波来实现的。在数值上，该研究是在具有随机定位的微孔洞的弹性材料上进行的。使用时域有限差分法。结果：实验发现，在低功率状态下，非线性超声波可以有效地检测到由于在 40% 蠕变寿命之前形成的微孔洞造成的材料损坏。观察到二阶非线性参数随蠕变寿命百分比的增加以及微孔洞浓度的相应增加。光学金相和显微硬度测量用于证实实验结果。对于数值研究，选择用于研究的空隙尺寸远低于探测波长。微孔的浓度从 0.01% 到 3% 不等。二阶非线性参数在初始阶段略有增加，并在模拟中随着微空隙浓度的升高而突然增加。这与实验趋势一致。结论：实验证明了使用非线性超声波在蠕变早期检测微孔洞的可行性，并通过数值研究了一个简单的孔洞模型，以显示二阶非线性参数对微孔洞的敏感性。选择用于研究的空隙尺寸远低于探测波长。微孔的浓度从 0.01% 到 3% 不等。二阶非线性参数在初始阶段略有增加，在模拟中随着微孔浓度的升高而突然增加。这与实验趋势一致。结论：实验证明了使用非线性超声波在蠕变早期检测微孔洞的可行性，并通过数值研究了一个简单的孔洞模型，以显示二阶非线性参数对微孔洞的敏感性。选择用于研究的空隙尺寸远低于探测波长。微孔的浓度从 0.01% 到 3% 不等。二阶非线性参数在初始阶段略有增加，并在模拟中随着微空隙浓度的升高而突然增加。这与实验趋势一致。结论：实验证明了使用非线性超声波在蠕变早期检测微孔洞的可行性，并通过数值研究了一个简单的空洞模型，以显示二阶非线性参数对微孔洞的敏感性。二阶非线性参数在初始阶段略有增加，并在模拟中随着微空隙浓度的升高而突然增加。这与实验趋势一致。结论：实验证明了使用非线性超声波在蠕变早期检测微孔洞的可行性，并通过数值研究了一个简单的空洞模型，以显示二阶非线性参数对微孔洞的敏感性。二阶非线性参数在初始阶段略有增加，并在模拟中随着微空隙浓度的升高而突然增加。这与实验趋势一致。结论：实验证明了使用非线性超声波在蠕变早期检测微孔洞的可行性，并通过数值研究了一个简单的孔洞模型，以显示二阶非线性参数对微孔洞的敏感性。