工程断裂中的T应力及其对裂纹扩展路径的影响
摘要
岩石、混凝土等工程材料中常含有裂纹这类缺陷,如何避免裂纹失稳扩展,导致整体结构的断裂,这是一个尤为重要的问题。裂纹的扩展主要是裂尖附近的应力集中所致。除了奇异项应力外,裂尖附近的常数项应力(即T应力)对材料中的裂纹扩展路径也起着决定性的作用。为了阐明工程材料中断裂参数与T应力之间的依赖关系,诠释裂纹扩展路径机理,在下列方面进行了比较深入而系统的理论分析和数值计算。
1.在光弹实验中利用应力-光学定律,推导出应力强度因子K和T应力与扩展裂纹尖端附近等差线条纹级数之间的非线性关系式,再借助求解非线性方程组的最小二乘法确定应力强度因子K和T应力。对T应力在扩展裂纹尖端应力场中的影响进行研究,发现T应力的大小和正负影响裂纹扩展尖端的光弹条纹的形状大小及倾斜度。因此在模拟裂纹扩展路径有必要考虑T应力的影响,并且对裂纹顶端的塑性区的小范围屈服修正时也有必要考虑T应力。
2.微裂纹尖端应力场中的T应力对裂纹扩展角和断裂韧度均有较大影响,这样造成传统最大周向应力断裂判据预测裂纹扩展角和断裂韧度结果偏差较大。本文提出了结合了T应力的修正最大周向应力断裂判据。在双轴压缩下的试件断裂中,将修正最大周向应力判据应用于模拟试件的压缩断裂。模拟扩展路径时,用指数函数来描述岩石类脆性材料中的裂纹粗糙界面退化,在扩展有限元模拟结果中发现结合了T应力判据的模拟结果和实验结果相一致。
3.在非定常热弹性单边裂纹无限长板断裂中,本文利用叠加原理,通过傅立叶转换,求解出奇异积分方程。从理论上分析了在非定常状态下的温度场中,裂纹尖端应力场中的应力强度因子和T应力分别与Biot数、裂纹长度及时间的关系。理论计算结果和有限元计算结果比较吻合。同时在热荷载作用下的PMMA材料的断裂实验中,结合T应力的有限元模拟值比较符合实验结果。
4.在混凝土三相材料中,引入弹簧层接触界面模型,理论计算得到了骨料和粘接层对应力强度因子和T应力影响,发现其对应力强度因子和T应力有很大的影响。由于T应力对裂尖塑性区有影响,通过建立双参数K-T模型来研究混凝土断裂的扩展路径和断裂韧度。在对Galve三点混凝土弯梁有限元模拟时,基于随机骨料结构,采用蒙特卡罗和Delaunay三角剖分原理,对混凝土试件随机骨料模型进行自动剖分,用三角形单元来模拟砂浆和骨料间的粘结带,并结合双参数K-T模型模型,模拟的裂纹扩展轨迹与试验结果获得的开裂轨迹范围吻合良好。
The crack is often contained in the rock, concrete and other engineering materials. It is particularly important problem that how to avoid the crack extension and finally result in fracture about the overall structure. Crack propagation is mainly caused by the stress concentration near the crack tip. In addition to the stress singularity, the constant term stress (ie. T-stress) that is near the crack also plays an important role in the crack propagation path. In order to clarify the relationship between the fracture parameters and T-stress, interpret of mechanism of crack propagation paths in the engineering materials, the in-depth and systematic theoretical analysis and numerical calculation are carried out. The main work includes the following parts:
1. In photoelastic experiments, the non-linear relationship between the stress intensity factor (ie. K), T-stress and line stripes arithmetic progression that near the crack tip are deduced by using stress-optical law. And then the stress intensity factors and T-stress are determined by solving nonlinear equations using the least squares method. Through research on T-stress that in the crack-tip stress field, it is found that the T-stress's sign and magnitude can affect the crack tip photoelastic fringe shape, size and inclination. Therefore, it is necessary to consider the impact of T-stress in simulating the crack propagation path. It is also necessary to consider T-stress's effect when the small scale yielding plastic zone that at the top of the crack is amended.
2. Because the micro-crack tip stress field's T-stress have a greater effect on the crack propagation angle and the fracture toughness, the results of crack growth and fracture toughness that are predicted by using traditional the maximum tangential (MTS) stress criterion have large deviations. The modified maximum tangential stress criterion that is combined with T-stress is presented. In biaxial compression fracture experiments, the modified MTS is applied to simulate the crack growth path. The exponential function is used to describe the rough interface degenerate of the rock's crack in the growth path simulated. It can be found that the modified MTS results by using the extended finite element method (XFEM) and the experimental results are consistent.
3. The crack's stress problem in the strip plate aroused by heat exchange in a difference of temperature field is studied. In this paper, the superposition principle and the Fourier transform are used, singular integral equation are solved. The crack tip stress field's the stress intensity factor and T-stress respectively relation about the Biot number, the crack length and time are analysed in the unsteady state temperature field. The analysis results and the finite element simulation results are consistent. In the heat loads of the PMMA material fracture experiments, the finite element simulation results that combination of T-stress are more consistent with experimental results.
4. In the three-phase materials concrete, the spring-layer interface model is introduced to calculate the stress intensity factor and T-stress when the influence of the aggregate and the bonding layer are considered. It is found that the aggregate and the bonding layer have great effect on the stress intensity factor and T-stress. Because the T-stress influence the crack tip plastic zone, the crack growth and the fracture toughness of the concrete are studied by using two-parameter K-T model. In this paper, the finite element simulate fracture about Galve concrete beam are completed. Because of based on the random aggregate, the concrete specimens random aggregate model are automatic partitioned by using the Monte Carlo and the Delaunay triangulation principle. The junction zone the between the mortar and aggregate is used by triangular element. The simulations of crack growth trajectory are consistent with the range of test results.
1.在光弹实验中利用应力-光学定律,推导出应力强度因子K和T应力与扩展裂纹尖端附近等差线条纹级数之间的非线性关系式,再借助求解非线性方程组的最小二乘法确定应力强度因子K和T应力。对T应力在扩展裂纹尖端应力场中的影响进行研究,发现T应力的大小和正负影响裂纹扩展尖端的光弹条纹的形状大小及倾斜度。因此在模拟裂纹扩展路径有必要考虑T应力的影响,并且对裂纹顶端的塑性区的小范围屈服修正时也有必要考虑T应力。
2.微裂纹尖端应力场中的T应力对裂纹扩展角和断裂韧度均有较大影响,这样造成传统最大周向应力断裂判据预测裂纹扩展角和断裂韧度结果偏差较大。本文提出了结合了T应力的修正最大周向应力断裂判据。在双轴压缩下的试件断裂中,将修正最大周向应力判据应用于模拟试件的压缩断裂。模拟扩展路径时,用指数函数来描述岩石类脆性材料中的裂纹粗糙界面退化,在扩展有限元模拟结果中发现结合了T应力判据的模拟结果和实验结果相一致。
3.在非定常热弹性单边裂纹无限长板断裂中,本文利用叠加原理,通过傅立叶转换,求解出奇异积分方程。从理论上分析了在非定常状态下的温度场中,裂纹尖端应力场中的应力强度因子和T应力分别与Biot数、裂纹长度及时间的关系。理论计算结果和有限元计算结果比较吻合。同时在热荷载作用下的PMMA材料的断裂实验中,结合T应力的有限元模拟值比较符合实验结果。
4.在混凝土三相材料中,引入弹簧层接触界面模型,理论计算得到了骨料和粘接层对应力强度因子和T应力影响,发现其对应力强度因子和T应力有很大的影响。由于T应力对裂尖塑性区有影响,通过建立双参数K-T模型来研究混凝土断裂的扩展路径和断裂韧度。在对Galve三点混凝土弯梁有限元模拟时,基于随机骨料结构,采用蒙特卡罗和Delaunay三角剖分原理,对混凝土试件随机骨料模型进行自动剖分,用三角形单元来模拟砂浆和骨料间的粘结带,并结合双参数K-T模型模型,模拟的裂纹扩展轨迹与试验结果获得的开裂轨迹范围吻合良好。
The crack is often contained in the rock, concrete and other engineering materials. It is particularly important problem that how to avoid the crack extension and finally result in fracture about the overall structure. Crack propagation is mainly caused by the stress concentration near the crack tip. In addition to the stress singularity, the constant term stress (ie. T-stress) that is near the crack also plays an important role in the crack propagation path. In order to clarify the relationship between the fracture parameters and T-stress, interpret of mechanism of crack propagation paths in the engineering materials, the in-depth and systematic theoretical analysis and numerical calculation are carried out. The main work includes the following parts:
1. In photoelastic experiments, the non-linear relationship between the stress intensity factor (ie. K), T-stress and line stripes arithmetic progression that near the crack tip are deduced by using stress-optical law. And then the stress intensity factors and T-stress are determined by solving nonlinear equations using the least squares method. Through research on T-stress that in the crack-tip stress field, it is found that the T-stress's sign and magnitude can affect the crack tip photoelastic fringe shape, size and inclination. Therefore, it is necessary to consider the impact of T-stress in simulating the crack propagation path. It is also necessary to consider T-stress's effect when the small scale yielding plastic zone that at the top of the crack is amended.
2. Because the micro-crack tip stress field's T-stress have a greater effect on the crack propagation angle and the fracture toughness, the results of crack growth and fracture toughness that are predicted by using traditional the maximum tangential (MTS) stress criterion have large deviations. The modified maximum tangential stress criterion that is combined with T-stress is presented. In biaxial compression fracture experiments, the modified MTS is applied to simulate the crack growth path. The exponential function is used to describe the rough interface degenerate of the rock's crack in the growth path simulated. It can be found that the modified MTS results by using the extended finite element method (XFEM) and the experimental results are consistent.
3. The crack's stress problem in the strip plate aroused by heat exchange in a difference of temperature field is studied. In this paper, the superposition principle and the Fourier transform are used, singular integral equation are solved. The crack tip stress field's the stress intensity factor and T-stress respectively relation about the Biot number, the crack length and time are analysed in the unsteady state temperature field. The analysis results and the finite element simulation results are consistent. In the heat loads of the PMMA material fracture experiments, the finite element simulation results that combination of T-stress are more consistent with experimental results.
4. In the three-phase materials concrete, the spring-layer interface model is introduced to calculate the stress intensity factor and T-stress when the influence of the aggregate and the bonding layer are considered. It is found that the aggregate and the bonding layer have great effect on the stress intensity factor and T-stress. Because the T-stress influence the crack tip plastic zone, the crack growth and the fracture toughness of the concrete are studied by using two-parameter K-T model. In this paper, the finite element simulate fracture about Galve concrete beam are completed. Because of based on the random aggregate, the concrete specimens random aggregate model are automatic partitioned by using the Monte Carlo and the Delaunay triangulation principle. The junction zone the between the mortar and aggregate is used by triangular element. The simulations of crack growth trajectory are consistent with the range of test results.
引文
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