裂纹扩展机理研究及管板开裂的数值模拟
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摘要
断裂是工程材料的主要失效形式,一些严重的断裂问题在化工设备中经常发生,为了防止或减少断裂现象的发生,必须对裂纹扩展的机理进行研究,人们按照裂纹的变形将裂纹分为三种基本形式,但是在工程实际中,大多数裂纹是由基本裂纹形式组成的复合型裂纹,因此,还必须研究裂纹转型问题。本文从微观和宏观两个方面对裂纹起裂和扩展的机理进行研究,并结合工程实践对换热器中的管板开裂进行模拟分析。
首先从微观上对Ⅰ型和Ⅱ型裂纹尖端的塑性区和无位错区形状和大小进行了模拟并分析了塑性区和无位错区对裂纹扩展的影响。结果表明,与宏观断裂力学算出的塑性区形状相比,本文给出的Ⅰ型塑性区向裂纹前方倾斜,无位错区的形状与塑性区相似,但是随着位错的发射,塑性区越来越大,无位错区越来越小；并以应变能密度因子理论为判据,得出当存在明显的无位错区时,塑性区使裂纹扩展的潜力下降,但扩展方向不变；而当塑性区充分发展、无位错区的作用减小或消失后,裂纹扩展的方向可能发生变化。Ⅱ型裂纹塑性区形状与应用线弹性裂纹前端应力场按von Mises屈服准则求得的Ⅱ型裂纹塑性区形状有所不同,本研究得出的Ⅱ型裂纹塑性区由三部分组成,且最大部分位于裂纹前方,裂尖周围无位错区形状与塑性区形状相似；从Ⅱ型裂纹裂尖发射的位错能够有效地屏蔽施加在裂纹上的外载荷,但发射出的位错偶对裂纹没有明显的屏蔽作用。随着Ⅱ型裂纹裂尖位错的发射或塑性区的发展,裂纹扩展变得越来越困难,而裂纹潜在的扩展方向不会改变。
其次从宏观上对带侧斜裂纹的紧凑拉伸试件进行了疲劳裂纹扩展的实验研究和裂纹尖端应力强度因子的数值计算,研究了复合型裂纹的转型扩展问题。结果发现,随着裂纹扩展,侧斜裂纹表面逐渐转向与外载荷垂直的方向,意味着裂纹从Ⅰ+Ⅲ复合型逐渐向Ⅰ型裂纹转化,且侧斜角越大,裂纹转型越快；对于不同侧斜角试件,Ⅲ型应力强度因子是不同的,但是Ⅰ型应力强度因子变化不大。裂纹转型主要由Ⅲ型成分控制,其转型速率可以表示成Ⅲ型应力强度因子相对幅值的函数；而疲劳裂纹扩展速率主要由Ⅰ型成分控制。
然后,对疲劳试件进行断面分析,研究复合型裂纹转型扩展过程中断口形貌的变化以及和裂纹组分之间的关系。结果发现,三种试件疲劳断口的疲劳源呈多源性,裂纹均萌生于紧凑拉伸试件线切割缺口处的微裂纹。与裂纹面不侧斜的标准试件相比,带侧斜角裂纹试件断面在疲劳源区形成了更为粗大的撕裂棱,不同撕裂棱之间的台阶形成了侧斜角试件的线切割斜面；转型过程中试件的断裂面较为粗糙,断口上存在较为粗大的撕裂棱和二次裂纹,而且在二次裂纹周围出现了分支裂纹,说明Ⅲ型成分的存在促进了二次裂纹和撕裂棱的形成。转型后试件的断裂面相对平坦,试件表面的撕裂棱和二次裂纹尺寸变细。
最后对一管壳式换热器管板开裂原因进行了研究。建立了液压胀接接头的三维有限元模型,模拟了液压胀接过程并得到了管板中的胀接残余应力；建立了含裂纹管板有限元模型,研究了在液压胀接残余应力或横向压力作用下裂纹沿厚度或管桥方向发生穿透性扩展的可能性。结果发现,在胀接残余应力作用下,不管沿管板厚度还是管桥方向裂纹始终保持张开状态,而横向载荷作用下,在弯曲压应力作用区域内,沿管板厚度和管桥方向的裂纹处于闭合状态,因此,胀接残余应力可能是形成贯穿管板厚度裂纹的原因。
Fracture is a major failure form of engineering materals which could lead to serious incidents with lots of loses especially in the chemical industries. In order to avoid or reduce fracture, crack initiation and propagation mechanisms must be understood. Three basic crack modes have been defined according to crack deformation. But most cracks in engineering are mixed-mode combined by the three basic crack modes. Crack mode transformation is a complicated problem which has to be addressed academically. In this dissertation, studies on crack propagation mechanisms have been carried out from macroscopic and microscopic point of view and tubesheet cracking in a practical heat-exchanger has been simulated to find the possible causes for the cracking.
Firstly, edge dislocation emissions from a ModeⅠor ModeⅡcrack tip along multiple inclined slip planes were simulated, and plastic zones as well as dislocation- free zones were obtained. It is found that the shape of the mode plastic zone is similar to that obtained by von Mises or Tresea yielding criterion but leaning forward from the crack tip. The shape of dislocation-free zone is similar to that of plastie zone. With dislocation emission, the plastic zone becomes larger and larger while the dislocation-free zone is getting smaller and smaller. Judged by the Strain energy density factor, the crack propagation potential decreases remarkably with dislocation emission. When a clear dislocation-free zone exists, the crack potential propagation direction will keep along the crack surface. However, when the plastic zone is fully developed or the dislocation-zone is vanished, the crack potential propagation direction may also be changed. The shape of plastic zone of ModeⅡis different from that based on von Mises. It is composed of three parts, and the most lies in front of the crack. There is a dislocation-free zone around the crack tip which has similar shape as the plastic zone. Dislocation emitting from the ModeⅡcrack are more effective in the shielding of the crack from the external loadings while dislocations coming from dislocation dipoles have no obvious shielding effeects. With dislocation emission or the development of plastic zone in front of the ModeⅡcrack tip, crack propagation becomes more difficult while the direction of the crack potential propagation may not be changed.
Secondly, compact tension specimens with tilt cracks under monotonic fatigue loadings were tested to investigateⅠ+Ⅲmixed mode fatigue crack propagation in the material of #45 steel with the stress on the mode transformation and crack propagation rate. It is found that with the crack growth,Ⅰ+Ⅲmixed mode changes to modeⅠand the larger the tilt angle or the larger the component of modeⅢ. Crack mode transformation is governed by the ModeⅢcomponent and the transformation rate is a function of the relative magnitude of the ModeⅢstress intensity factor. Even in the process of the crack mode transformation, the fatigue crack propagation is controlled by the ModeⅠdeformation.
Thirdly, Fracture surfaces of the fatigue test specimens were examined to investigate the fractography changes corresponding to the crack mode transformation. Results show that the fatigue cracks propagate with multi-sources initiated from micro-cracks on the line-cutting notch of the compact tension specimens. The tilted crack surface is rougher than that without tilting by presenting more tear ridges which actually contribute the tilt of the crack surface. Striations on the surface without tilting are more continuous while more secondary cracks are found on the tilted crack surfaces. With the crack mode transformation the fracture surfaces with different tilted cracks become more and more identical. So it can be reached that the Mode III component is responsible for the formation of the rough surface and secondary cracks.
Finally, possible cracking causes for a tubesheet in a real heat exchanger have been analysed. A 3-D finite element model for a hydraulically expanded tube-to-tubesheet joint was established and the expansion process was simulated to obtain the residual stress in the tubesheet. Finite element model for a tubesheet with crack was also set up to investgate the possibility of crack propagation through thickness or tube-bridge. It is found that under the action of the residual stress induced by expansion, a crack along the tubesheet thickness or tube-bridge keeps open while it will close in the compressive region under the action of transversed pressure loading. So it seems that the residual expansion stress could be the driving force for the tubesheet cracking through the thickness.
首先从微观上对Ⅰ型和Ⅱ型裂纹尖端的塑性区和无位错区形状和大小进行了模拟并分析了塑性区和无位错区对裂纹扩展的影响。结果表明,与宏观断裂力学算出的塑性区形状相比,本文给出的Ⅰ型塑性区向裂纹前方倾斜,无位错区的形状与塑性区相似,但是随着位错的发射,塑性区越来越大,无位错区越来越小；并以应变能密度因子理论为判据,得出当存在明显的无位错区时,塑性区使裂纹扩展的潜力下降,但扩展方向不变；而当塑性区充分发展、无位错区的作用减小或消失后,裂纹扩展的方向可能发生变化。Ⅱ型裂纹塑性区形状与应用线弹性裂纹前端应力场按von Mises屈服准则求得的Ⅱ型裂纹塑性区形状有所不同,本研究得出的Ⅱ型裂纹塑性区由三部分组成,且最大部分位于裂纹前方,裂尖周围无位错区形状与塑性区形状相似；从Ⅱ型裂纹裂尖发射的位错能够有效地屏蔽施加在裂纹上的外载荷,但发射出的位错偶对裂纹没有明显的屏蔽作用。随着Ⅱ型裂纹裂尖位错的发射或塑性区的发展,裂纹扩展变得越来越困难,而裂纹潜在的扩展方向不会改变。
其次从宏观上对带侧斜裂纹的紧凑拉伸试件进行了疲劳裂纹扩展的实验研究和裂纹尖端应力强度因子的数值计算,研究了复合型裂纹的转型扩展问题。结果发现,随着裂纹扩展,侧斜裂纹表面逐渐转向与外载荷垂直的方向,意味着裂纹从Ⅰ+Ⅲ复合型逐渐向Ⅰ型裂纹转化,且侧斜角越大,裂纹转型越快；对于不同侧斜角试件,Ⅲ型应力强度因子是不同的,但是Ⅰ型应力强度因子变化不大。裂纹转型主要由Ⅲ型成分控制,其转型速率可以表示成Ⅲ型应力强度因子相对幅值的函数；而疲劳裂纹扩展速率主要由Ⅰ型成分控制。
然后,对疲劳试件进行断面分析,研究复合型裂纹转型扩展过程中断口形貌的变化以及和裂纹组分之间的关系。结果发现,三种试件疲劳断口的疲劳源呈多源性,裂纹均萌生于紧凑拉伸试件线切割缺口处的微裂纹。与裂纹面不侧斜的标准试件相比,带侧斜角裂纹试件断面在疲劳源区形成了更为粗大的撕裂棱,不同撕裂棱之间的台阶形成了侧斜角试件的线切割斜面；转型过程中试件的断裂面较为粗糙,断口上存在较为粗大的撕裂棱和二次裂纹,而且在二次裂纹周围出现了分支裂纹,说明Ⅲ型成分的存在促进了二次裂纹和撕裂棱的形成。转型后试件的断裂面相对平坦,试件表面的撕裂棱和二次裂纹尺寸变细。
最后对一管壳式换热器管板开裂原因进行了研究。建立了液压胀接接头的三维有限元模型,模拟了液压胀接过程并得到了管板中的胀接残余应力；建立了含裂纹管板有限元模型,研究了在液压胀接残余应力或横向压力作用下裂纹沿厚度或管桥方向发生穿透性扩展的可能性。结果发现,在胀接残余应力作用下,不管沿管板厚度还是管桥方向裂纹始终保持张开状态,而横向载荷作用下,在弯曲压应力作用区域内,沿管板厚度和管桥方向的裂纹处于闭合状态,因此,胀接残余应力可能是形成贯穿管板厚度裂纹的原因。
Fracture is a major failure form of engineering materals which could lead to serious incidents with lots of loses especially in the chemical industries. In order to avoid or reduce fracture, crack initiation and propagation mechanisms must be understood. Three basic crack modes have been defined according to crack deformation. But most cracks in engineering are mixed-mode combined by the three basic crack modes. Crack mode transformation is a complicated problem which has to be addressed academically. In this dissertation, studies on crack propagation mechanisms have been carried out from macroscopic and microscopic point of view and tubesheet cracking in a practical heat-exchanger has been simulated to find the possible causes for the cracking.
Firstly, edge dislocation emissions from a ModeⅠor ModeⅡcrack tip along multiple inclined slip planes were simulated, and plastic zones as well as dislocation- free zones were obtained. It is found that the shape of the mode plastic zone is similar to that obtained by von Mises or Tresea yielding criterion but leaning forward from the crack tip. The shape of dislocation-free zone is similar to that of plastie zone. With dislocation emission, the plastic zone becomes larger and larger while the dislocation-free zone is getting smaller and smaller. Judged by the Strain energy density factor, the crack propagation potential decreases remarkably with dislocation emission. When a clear dislocation-free zone exists, the crack potential propagation direction will keep along the crack surface. However, when the plastic zone is fully developed or the dislocation-zone is vanished, the crack potential propagation direction may also be changed. The shape of plastic zone of ModeⅡis different from that based on von Mises. It is composed of three parts, and the most lies in front of the crack. There is a dislocation-free zone around the crack tip which has similar shape as the plastic zone. Dislocation emitting from the ModeⅡcrack are more effective in the shielding of the crack from the external loadings while dislocations coming from dislocation dipoles have no obvious shielding effeects. With dislocation emission or the development of plastic zone in front of the ModeⅡcrack tip, crack propagation becomes more difficult while the direction of the crack potential propagation may not be changed.
Secondly, compact tension specimens with tilt cracks under monotonic fatigue loadings were tested to investigateⅠ+Ⅲmixed mode fatigue crack propagation in the material of #45 steel with the stress on the mode transformation and crack propagation rate. It is found that with the crack growth,Ⅰ+Ⅲmixed mode changes to modeⅠand the larger the tilt angle or the larger the component of modeⅢ. Crack mode transformation is governed by the ModeⅢcomponent and the transformation rate is a function of the relative magnitude of the ModeⅢstress intensity factor. Even in the process of the crack mode transformation, the fatigue crack propagation is controlled by the ModeⅠdeformation.
Thirdly, Fracture surfaces of the fatigue test specimens were examined to investigate the fractography changes corresponding to the crack mode transformation. Results show that the fatigue cracks propagate with multi-sources initiated from micro-cracks on the line-cutting notch of the compact tension specimens. The tilted crack surface is rougher than that without tilting by presenting more tear ridges which actually contribute the tilt of the crack surface. Striations on the surface without tilting are more continuous while more secondary cracks are found on the tilted crack surfaces. With the crack mode transformation the fracture surfaces with different tilted cracks become more and more identical. So it can be reached that the Mode III component is responsible for the formation of the rough surface and secondary cracks.
Finally, possible cracking causes for a tubesheet in a real heat exchanger have been analysed. A 3-D finite element model for a hydraulically expanded tube-to-tubesheet joint was established and the expansion process was simulated to obtain the residual stress in the tubesheet. Finite element model for a tubesheet with crack was also set up to investgate the possibility of crack propagation through thickness or tube-bridge. It is found that under the action of the residual stress induced by expansion, a crack along the tubesheet thickness or tube-bridge keeps open while it will close in the compressive region under the action of transversed pressure loading. So it seems that the residual expansion stress could be the driving force for the tubesheet cracking through the thickness.
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