Pub Date : 2024-02-20DOI: 10.1007/s10704-023-00757-0
Abstract
A novel fatigue model under Cosserat peridynamic framework is proposed to investigate concrete fatigue performance. In this model, a novel cyclic bond failure criterion is established to measure the combined tension/compressive-shear fatigue failure in concrete, which is derived from the Bresler-Pister criterion. Three benchmarks with different fatigue crack modes in concrete are designed. Results show that the mode I and mixed mode I-II fatigue crack patterns are predicted. In the three-point-bend beam fatigue test, the numerical result matches well with the experimental result, in the uniaxial compressive fatigue test, the effects of Cosserat parameters on fatigue crack patterns are discussed. Results found that the Cosserat parameters reflect the effects of concrete microstructures on crack patterns, and the larger Cosserat shear modulus accelerates the fatigue crack propagation process.
{"title":"A fatigue model under Cosserat peridynamic framework for concrete fatigue cracking","authors":"","doi":"10.1007/s10704-023-00757-0","DOIUrl":"https://doi.org/10.1007/s10704-023-00757-0","url":null,"abstract":"<h3>Abstract</h3> <p>A novel fatigue model under Cosserat peridynamic framework is proposed to investigate concrete fatigue performance. In this model, a novel cyclic bond failure criterion is established to measure the combined tension/compressive-shear fatigue failure in concrete, which is derived from the Bresler-Pister criterion. Three benchmarks with different fatigue crack modes in concrete are designed. Results show that the mode I and mixed mode I-II fatigue crack patterns are predicted. In the three-point-bend beam fatigue test, the numerical result matches well with the experimental result, in the uniaxial compressive fatigue test, the effects of Cosserat parameters on fatigue crack patterns are discussed. Results found that the Cosserat parameters reflect the effects of concrete microstructures on crack patterns, and the larger Cosserat shear modulus accelerates the fatigue crack propagation process.</p>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139910320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-19DOI: 10.1007/s10704-024-00769-4
F. Bobaru, U. Galvanetto, Ziguang Chen
{"title":"Introduction to the special issue on nonlocal models in fracture and damage","authors":"F. Bobaru, U. Galvanetto, Ziguang Chen","doi":"10.1007/s10704-024-00769-4","DOIUrl":"https://doi.org/10.1007/s10704-024-00769-4","url":null,"abstract":"","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140451466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Efficient and accurate prediction of chloride concentration distribution in concrete is extremely important for evaluating the durability of reinforced concrete (RC) structures in the coastal region. A peridynamic (PD) framework for chloride diffusion–reaction is proposed to explore the mechanisms of the long-term chloride ingress in concrete. Specifically, the improved intermediately homogenized peridynamic (IH-PD) method is substituted for the solid modeling method of the interface transition zone (ITZ), with the consideration of the mesoscopic characteristics of concrete and great computational efficiency. In addition, considering the effect of concrete mesostructure, an effective chloride diffusion coefficient is constructed based on the Mori–Tanaka method, in which the proportion of various bonds is determined by the statistics. To verify the reliability of the proposed model, the numerical results are compared with the third-party experiments data. From the results, the randomness of concrete mesostructure leads to the randomness of chloride concentration at the same ingress depth, following the normal distribution. Moreover, the chloride diffusion performance which reflects the speed of chloride diffusion is significantly improved with the increase in the water-cement ratio. Noteworthily, the ITZ thickness can be appropriately increased without affecting the reliability of the results.
{"title":"Peridynamic model for chloride diffusion–reaction in concrete reflecting mesostructure characteristic","authors":"Xuandong Chen, Xin Gu, Panyong Liu, Jiamin Zhang, Xiaozhou Xia, Qing Zhang","doi":"10.1007/s10704-023-00760-5","DOIUrl":"https://doi.org/10.1007/s10704-023-00760-5","url":null,"abstract":"<p>Efficient and accurate prediction of chloride concentration distribution in concrete is extremely important for evaluating the durability of reinforced concrete (RC) structures in the coastal region. A peridynamic (PD) framework for chloride diffusion–reaction is proposed to explore the mechanisms of the long-term chloride ingress in concrete. Specifically, the improved intermediately homogenized peridynamic (IH-PD) method is substituted for the solid modeling method of the interface transition zone (ITZ), with the consideration of the mesoscopic characteristics of concrete and great computational efficiency. In addition, considering the effect of concrete mesostructure, an effective chloride diffusion coefficient is constructed based on the Mori–Tanaka method, in which the proportion of various bonds is determined by the statistics. To verify the reliability of the proposed model, the numerical results are compared with the third-party experiments data. From the results, the randomness of concrete mesostructure leads to the randomness of chloride concentration at the same ingress depth, following the normal distribution. Moreover, the chloride diffusion performance which reflects the speed of chloride diffusion is significantly improved with the increase in the water-cement ratio. Noteworthily, the ITZ thickness can be appropriately increased without affecting the reliability of the results.</p>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139773604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-16DOI: 10.1007/s10704-023-00758-z
Yehui Bie, Kuanjie Ding, Zhifu Zhao, Yueguang Wei
The peridynamic correspondence model (PDCM) provides the stress–strain relation that can introduce many classical constitutive models, however, the high computational consumption and zero-energy mode of PDCM certainly limit its further application to practical engineering crack problems. To solve these limitations and exploit the advantage of PDCM, we propose a simple and effective method that adaptively couples dual-horizon peridynamic element (DH-PDE) with finite element (FE) to simulate the quasi-static fracture problems. To this end, a stabilized dual-horizon peridynamic element for DH-PDCM is firstly developed that the peridynamic strain matrices for the bond and material point are constructed respectively. The nonlocal ordinary and correctional peridynamic element stiffness matrices are derived in detail and calculated by the proposed dual-assembly algorithm. Subsequently, a unified variational weak form of this adaptive coupling of DH-PDE and FE is proposed based on the convergence of peridynamics to the classical model in the limit of vanishing horizon. Therefore, the integrals of the peridynamic element and finite element in this coupling method are completely decoupled in the viewpoint of numerical implementation, which makes it easier to realize the proposed adaptive coupling by switching integral element. Moreover, the proposed adaptive coupling is implemented in Abaqus/UEL to optimize the calculational efficiency and real-time visualization of calculated results, which has potential for dealing with the engineering crack problems. Two-dimensional numerical examples involving mode-I and mixed-mode crack problems are used to demonstrate the effectiveness of this adaptive coupling in addressing the quasi-static fracture of cohesive materials.
周动态对应模型(PDCM)提供的应力应变关系可以引入许多经典的构成模型,然而,PDCM 的高计算消耗和零能量模式无疑限制了其在实际工程裂缝问题中的进一步应用。为了解决这些限制并发挥 PDCM 的优势,我们提出了一种简单有效的方法,将双水平周动态元素 (DH-PDE) 与有限元 (FE) 自适应地结合起来,模拟准静态断裂问题。为此,首先开发了用于 DH-PDCM 的稳定双水平围动元,并分别构建了结合点和材料点的围动应变矩阵。详细推导了非局部普通围动力元素刚度矩阵和修正围动力元素刚度矩阵,并通过所提出的双装配算法进行了计算。随后,基于围动力学在消失视界极限下对经典模型的收敛性,提出了 DH-PDE 和 FE 自适应耦合的统一变分弱形式。因此,从数值实现的角度来看,这种耦合方法中的周动力学元素和有限元的积分是完全解耦的,这使得通过切换积分元素来实现所提出的自适应耦合变得更加容易。此外,提出的自适应耦合在 Abaqus/UEL 中实现,优化了计算效率和计算结果的实时可视化,具有处理工程裂缝问题的潜力。涉及 I 模式和混合模式裂纹问题的二维数值示例证明了自适应耦合在处理内聚材料准静态断裂方面的有效性。
{"title":"The adaptive coupling of dual-horizon peridynamic element and finite element for the progressive failure of materials","authors":"Yehui Bie, Kuanjie Ding, Zhifu Zhao, Yueguang Wei","doi":"10.1007/s10704-023-00758-z","DOIUrl":"https://doi.org/10.1007/s10704-023-00758-z","url":null,"abstract":"<p>The peridynamic correspondence model (PDCM) provides the stress–strain relation that can introduce many classical constitutive models, however, the high computational consumption and zero-energy mode of PDCM certainly limit its further application to practical engineering crack problems. To solve these limitations and exploit the advantage of PDCM, we propose a simple and effective method that adaptively couples dual-horizon peridynamic element (DH-PDE) with finite element (FE) to simulate the quasi-static fracture problems. To this end, a stabilized dual-horizon peridynamic element for DH-PDCM is firstly developed that the peridynamic strain matrices for the bond and material point are constructed respectively. The nonlocal ordinary and correctional peridynamic element stiffness matrices are derived in detail and calculated by the proposed dual-assembly algorithm. Subsequently, a unified variational weak form of this adaptive coupling of DH-PDE and FE is proposed based on the convergence of peridynamics to the classical model in the limit of vanishing horizon. Therefore, the integrals of the peridynamic element and finite element in this coupling method are completely decoupled in the viewpoint of numerical implementation, which makes it easier to realize the proposed adaptive coupling by switching integral element. Moreover, the proposed adaptive coupling is implemented in Abaqus/UEL to optimize the calculational efficiency and real-time visualization of calculated results, which has potential for dealing with the engineering crack problems. Two-dimensional numerical examples involving mode-I and mixed-mode crack problems are used to demonstrate the effectiveness of this adaptive coupling in addressing the quasi-static fracture of cohesive materials.</p>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139767214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-15DOI: 10.1007/s10704-024-00762-x
Abstract
A multi-phase-field approach for crack propagation considering the contribution of the interface energy is presented. The interface energy is either the grain boundary energy or the energy between a pair of solid phases and is directly incorporated into to the Ginzburg–Landau equation for fracture. The finite difference method is utilized to solve the crack phase-field evolution equation and fast Fourier method is used to solve the mechanical equilibrium equation in three dimensions for a polycrystalline material. The importance of the interface (grain boundary) energy is analyzed numerically for various model problems. The results show how the interface energy variations change the crack trajectory between the intergranular and transgranular fracture.
{"title":"Multi-phase-field approach to fracture demonstrating the role of solid-solid interface energy on crack propagation","authors":"","doi":"10.1007/s10704-024-00762-x","DOIUrl":"https://doi.org/10.1007/s10704-024-00762-x","url":null,"abstract":"<h3>Abstract</h3> <p>A multi-phase-field approach for crack propagation considering the contribution of the interface energy is presented. The interface energy is either the grain boundary energy or the energy between a pair of solid phases and is directly incorporated into to the Ginzburg–Landau equation for fracture. The finite difference method is utilized to solve the crack phase-field evolution equation and fast Fourier method is used to solve the mechanical equilibrium equation in three dimensions for a polycrystalline material. The importance of the interface (grain boundary) energy is analyzed numerically for various model problems. The results show how the interface energy variations change the crack trajectory between the intergranular and transgranular fracture.</p>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139767305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-23DOI: 10.1007/s10704-023-00755-2
Arnaud Coq, Julie Diani, Stella Brach
Brittle material Mode I fracture may be characterized by the double cleavage drilled compression test. For linear elastic materials, the critical energy release rate, or fracture toughness, can be estimated simply using the linear elastic fracture mechanics. For other types of constitutive behavior, the material parameter has to be determined with numerical fracture modeling. In this paper, we have used two approaches, the phase-field damage model and the cohesive elements, in order to estimate the critical energy release rate of an elastoplastic material. Firstly, we assessed the numerical models and discussed their parameters by comparison of available data from double cleavage drilled compression experimental tests run on a silica glass. Both phase-field damage and cohesive zone models were able to reproduce fracture initiation at the observed macroscopic stress for the linear elastic material. However, the material toughness could not be predicted by the phase-field approach due to the result dependence on the model regularization parameter. Secondly, an elastoplastic methyl methacrylate polymer was submitted to the compression test in our lab. Both models were then extended for elastic-perfectly plastic materials. Crack initiation was obtained at the observed macroscopic strain for similar critical energy release rate ranges for both approaches, providing good confidence in the estimated material toughness.
脆性材料的 I 型断裂可通过双劈裂钻孔压缩试验来表征。对于线性弹性材料,临界能量释放率或断裂韧性可通过线性弹性断裂力学简单估算。对于其他类型的构成行为,材料参数必须通过数值断裂模型来确定。在本文中,我们采用了相场损伤模型和内聚元素两种方法来估算弹塑性材料的临界能量释放率。首先,我们对数值模型进行了评估,并通过对比硅玻璃双劈钻孔压缩实验测试的可用数据讨论了模型参数。相场损伤模型和内聚区模型都能再现线性弹性材料在观测到的宏观应力下的断裂起始。然而,由于结果取决于模型正则化参数,相场方法无法预测材料的韧性。其次,我们在实验室对一种弹性甲基丙烯酸甲酯聚合物进行了压缩试验。然后将这两个模型扩展到弹性全塑材料。在两种方法的临界能量释放率范围相似的情况下,在观察到的宏观应变处都出现了裂纹起始,这为估计材料韧性提供了很好的可信度。
{"title":"Comparison of the phase-field approach and cohesive element modeling to analyze the double cleavage drilled compression fracture test of an elastoplastic material","authors":"Arnaud Coq, Julie Diani, Stella Brach","doi":"10.1007/s10704-023-00755-2","DOIUrl":"https://doi.org/10.1007/s10704-023-00755-2","url":null,"abstract":"<p>Brittle material Mode I fracture may be characterized by the double cleavage drilled compression test. For linear elastic materials, the critical energy release rate, or fracture toughness, can be estimated simply using the linear elastic fracture mechanics. For other types of constitutive behavior, the material parameter has to be determined with numerical fracture modeling. In this paper, we have used two approaches, the phase-field damage model and the cohesive elements, in order to estimate the critical energy release rate of an elastoplastic material. Firstly, we assessed the numerical models and discussed their parameters by comparison of available data from double cleavage drilled compression experimental tests run on a silica glass. Both phase-field damage and cohesive zone models were able to reproduce fracture initiation at the observed macroscopic stress for the linear elastic material. However, the material toughness could not be predicted by the phase-field approach due to the result dependence on the model regularization parameter. Secondly, an elastoplastic methyl methacrylate polymer was submitted to the compression test in our lab. Both models were then extended for elastic-perfectly plastic materials. Crack initiation was obtained at the observed macroscopic strain for similar critical energy release rate ranges for both approaches, providing good confidence in the estimated material toughness.</p>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139558356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-06DOI: 10.1007/s10704-023-00754-3
Jonas Rudshaug, Tore Børvik, Odd Sture Hopperstad
Brittle materials are known for their violent and unpredictable cracking behavior. A behavior which is dictated by a combination of microscopical material defects and the competition between the potential energy of the system and the surface energy of the material. In this study, we present the implementation of a dynamic fracture phase-field model with a new crack driving force into a commercial finite element (FE) solver and examine its behavior using three different tension-compression splits. After validating the implementation, we use the model to investigate its predictive capacity on quasi-statically loaded L-shaped soda-lime glass specimens with varying critical load levels. The dynamic fracture phase-field model predicted similar crack propagation to what was found in the literature for quasi-static and dynamic validation cases. By varying the critical load level for the L-shaped soda-lime glass specimens using the new crack driving force, the model predicted a positive correlation between the initial crack propagation speed and the critical load level, similar to what was seen in the experiments. However, the predicted crack propagation speed decreased quicker than the experimental crack propagation speed. The tension-compression splits had an impact on the predicted crack propagation paths. Overall, the proposed crack driving force used in the dynamic fracture phase-field model seems to capture the relation between critical load and initial crack propagation speed and thus enables crack predictions for specimens of varying strength.
脆性材料以其剧烈和不可预测的开裂行为而闻名。这种行为是由微观材料缺陷以及系统势能和材料表面能之间的竞争共同决定的。在本研究中,我们介绍了如何在商用有限元(FE)求解器中实施带有新裂纹驱动力的动态断裂相场模型,并使用三种不同的拉伸-压缩分裂来检验其行为。在验证了该模型的实施后,我们使用该模型研究了其对具有不同临界载荷水平的准静载 L 型钠钙玻璃试样的预测能力。在准静态和动态验证情况下,动态断裂相场模型预测的裂纹扩展与文献中的结果相似。通过使用新的裂纹驱动力改变 L 形钠长石玻璃试样的临界载荷水平,该模型预测了初始裂纹扩展速度与临界载荷水平之间的正相关关系,这与实验中的结果类似。然而,预测的裂纹扩展速度比实验的裂纹扩展速度下降得更快。拉伸-压缩分裂对预测的裂纹扩展路径有影响。总之,动态断裂相场模型中使用的裂纹驱动力似乎捕捉到了临界载荷与初始裂纹扩展速度之间的关系,因此可以对不同强度的试样进行裂纹预测。
{"title":"Modeling brittle crack propagation for varying critical load levels: a dynamic phase-field approach","authors":"Jonas Rudshaug, Tore Børvik, Odd Sture Hopperstad","doi":"10.1007/s10704-023-00754-3","DOIUrl":"https://doi.org/10.1007/s10704-023-00754-3","url":null,"abstract":"<p>Brittle materials are known for their violent and unpredictable cracking behavior. A behavior which is dictated by a combination of microscopical material defects and the competition between the potential energy of the system and the surface energy of the material. In this study, we present the implementation of a dynamic fracture phase-field model with a new crack driving force into a commercial finite element (FE) solver and examine its behavior using three different tension-compression splits. After validating the implementation, we use the model to investigate its predictive capacity on quasi-statically loaded L-shaped soda-lime glass specimens with varying critical load levels. The dynamic fracture phase-field model predicted similar crack propagation to what was found in the literature for quasi-static and dynamic validation cases. By varying the critical load level for the L-shaped soda-lime glass specimens using the new crack driving force, the model predicted a positive correlation between the initial crack propagation speed and the critical load level, similar to what was seen in the experiments. However, the predicted crack propagation speed decreased quicker than the experimental crack propagation speed. The tension-compression splits had an impact on the predicted crack propagation paths. Overall, the proposed crack driving force used in the dynamic fracture phase-field model seems to capture the relation between critical load and initial crack propagation speed and thus enables crack predictions for specimens of varying strength.</p>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139375626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-22DOI: 10.1007/s10704-023-00753-4
Min Xu, H. D. Wagner, Bingbing An
{"title":"An analysis of interfacial debonding in beaded fiber composites","authors":"Min Xu, H. D. Wagner, Bingbing An","doi":"10.1007/s10704-023-00753-4","DOIUrl":"https://doi.org/10.1007/s10704-023-00753-4","url":null,"abstract":"","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138945323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-14DOI: 10.1007/s10704-023-00752-5
A. G. Varias
Hydride precipitation ahead of a crack is examined under conditions of hydrogen chemical equilibrium, steady-state heat conduction and linear elastic metal behavior. The limiting conditions are approached via the interaction of the operating physical mechanisms of material deformation, hydrogen diffusion and energy flow. Analytical relations are presented for the distributions of hydrogen concentration in solid solution, hydride volume fraction and stress components, as well as for the hydride precipitation zone boundary. It is shown that there is an annulus, within the hydride precipitation zone, where stresses, although vary according to (1/sqrt{r})—singularity, deviate significantly from the well-known K-field, being smaller, according to the difference of hydrostatic stress before and after hydride precipitation. The hydride precipitation zone increases with crack-tip constraint, given by T-stress. In addition, temperature gradient affects hydride precipitation zone size, by controlling stress trace distribution.
在氢化学平衡、稳态热传导和线性弹性金属行为的条件下,对裂缝前的氢化物析出进行了研究。极限条件是通过材料变形、氢扩散和能量流等运行物理机制的相互作用来实现的。对固溶体中的氢浓度分布、氢化物体积分数和应力分量以及氢化物析出区边界提出了分析关系。结果表明,在氢化物析出区内有一个环形区域,该区域的应力虽然根据 (1/sqrt{r})-singularity 变化,但与众所周知的 K 场有明显偏差,根据氢化物析出前后静水压力的差异,该区域的应力较小。氢化物析出区随着裂纹尖端约束(由 T 应力给出)的增加而增大。此外,温度梯度通过控制应力轨迹分布影响氢化物析出区的大小。
{"title":"Elastic crack-tip field in hydride forming metals under hydrogen chemical equilibrium","authors":"A. G. Varias","doi":"10.1007/s10704-023-00752-5","DOIUrl":"https://doi.org/10.1007/s10704-023-00752-5","url":null,"abstract":"<p>Hydride precipitation ahead of a crack is examined under conditions of hydrogen chemical equilibrium, steady-state heat conduction and linear elastic metal behavior. The limiting conditions are approached via the interaction of the operating physical mechanisms of material deformation, hydrogen diffusion and energy flow. Analytical relations are presented for the distributions of hydrogen concentration in solid solution, hydride volume fraction and stress components, as well as for the hydride precipitation zone boundary. It is shown that there is an annulus, within the hydride precipitation zone, where stresses, although vary according to <span>(1/sqrt{r})</span>—singularity, deviate significantly from the well-known K-field, being smaller, according to the difference of hydrostatic stress before and after hydride precipitation. The hydride precipitation zone increases with crack-tip constraint, given by T-stress. In addition, temperature gradient affects hydride precipitation zone size, by controlling stress trace distribution.</p>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138681386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-01DOI: 10.1007/s10704-023-00751-6
Bangguo Zhu, Jikun Wang, Alan T. Zehnder, Chung-Yuen Hui
The Pure Shear (PS) crack specimen is widely employed to assess the fracture toughness of soft elastic materials. It serves as a valuable tool for investigating the behavior of crack growth in a steady-state manner following crack initiation. One of its advantages lies in the fact that the energy release rate (J) remains approximately constant for sufficiently long cracks, independent of crack length. Additionally, the PS specimen facilitates the easy evaluation of J for long cracks by means of a tension test conducted on an uncracked sample. However, the lack of a published expression for short cracks currently restricts the usefulness of this specimen. To overcome this limitation, we conducted a series of finite element (FE) simulations utilizing three different constitutive models, namely the neo-Hookean (NH), Arruda-Boyce (AB), and Mooney-Rivlin (MR) models. Our finite element analysis (FEA) encompassed practical crack lengths and strain levels. The results revealed that under a fixed applied displacement, the energy release rate (J) monotonically increases with the crack length for short cracks, reaches a steady-state value when the crack length exceeds the height of the specimen, and subsequently decreases as the crack approaches the end of the specimen. Drawing from these findings, we propose a simple closed-form expression for J that can be applied to most hyper-elastic models and is suitable for all practical crack lengths, particularly short cracks.
{"title":"Energy release rate of a mode-I crack in pure shear specimens subjected to large deformation","authors":"Bangguo Zhu, Jikun Wang, Alan T. Zehnder, Chung-Yuen Hui","doi":"10.1007/s10704-023-00751-6","DOIUrl":"https://doi.org/10.1007/s10704-023-00751-6","url":null,"abstract":"<p>The Pure Shear (PS) crack specimen is widely employed to assess the fracture toughness of soft elastic materials. It serves as a valuable tool for investigating the behavior of crack growth in a steady-state manner following crack initiation. One of its advantages lies in the fact that the energy release rate (<i>J</i>) remains approximately constant for sufficiently long cracks, independent of crack length. Additionally, the PS specimen facilitates the easy evaluation of <i>J</i> for long cracks by means of a tension test conducted on an uncracked sample. However, the lack of a published expression for short cracks currently restricts the usefulness of this specimen. To overcome this limitation, we conducted a series of finite element (FE) simulations utilizing three different constitutive models, namely the neo-Hookean (NH), Arruda-Boyce (AB), and Mooney-Rivlin (MR) models. Our finite element analysis (FEA) encompassed practical crack lengths and strain levels. The results revealed that under a fixed applied displacement, the energy release rate (<i>J</i>) monotonically increases with the crack length for short cracks, reaches a steady-state value when the crack length exceeds the height of the specimen, and subsequently decreases as the crack approaches the end of the specimen. Drawing from these findings, we propose a simple closed-form expression for <i>J</i> that can be applied to most hyper-elastic models and is suitable for all practical crack lengths, particularly short cracks.</p>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138510171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}