Engineering Fracture Mechanics最新文献

{"title":"Effective fracture toughness in phase-field models for interface fracture","authors":"Christopher A. Fear ,&nbsp;Simon Wang ,&nbsp;Christopher M. Harvey","doi":"10.1016/j.engfracmech.2025.111546","DOIUrl":"10.1016/j.engfracmech.2025.111546","url":null,"abstract":"<div><div>When applying the phase-field fracture model (PFFM) to interface fracture, the diffuse phase-field damage interferes with the surrounding bulk material, artificially increasing the apparent interface fracture toughness (assuming the bulk material has a higher fracture toughness). This effect can be mitigated by using an effective fracture toughness value. However, existing analytical expressions in the literature for effective fracture toughness neglect the history of tensile elastic strain energy during loading, which is shown here to be a crucial factor, even for a crack in a homogeneous material. In this work, the phase-field damage profile around an interface crack is derived from first principles, explicitly accounting for tensile elastic strain energy. The effective fracture toughness is then evaluated using a variation of the established energy dissipation balance approach. Finite-element method (FEM) simulations are conducted to model crack propagation in various configurations using the PFFM. First, the effective fracture toughness is determined empirically by tuning it until the apparent toughness matches the interface material’s fracture toughness. Second, the FEM results are compared against three new mathematical models developed in this work, and the current best model from the literature, considering effective fracture toughness and crack phase-field damage profiles. Although all the new mathematical models show good agreement with FEM results, one model in particular, which modifies sharp crack theory to approximate the tensile elastic strain energy in the PFFM, shows particularly strong agreement with FEM results in all regards, and outperforms models that disregard tensile elastic strain energy. This model can be used to accurately and efficiently pre-compute effective fracture toughness for PFFM simulations.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"328 ","pages":"Article 111546"},"PeriodicalIF":5.3,"publicationDate":"2025-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Enforcement of the irreversibility condition in the phase field damage model: Influence of the history variable approximation","authors":"Abdelmalek Barki ,&nbsp;Jihed Zghal ,&nbsp;Laurent Gallimard ,&nbsp;Isabelle Bruant ,&nbsp;Nicolas Chevaugeon ,&nbsp;Luc Davenne","doi":"10.1016/j.engfracmech.2025.111518","DOIUrl":"10.1016/j.engfracmech.2025.111518","url":null,"abstract":"<div><div>The phase field damage model has been widely used in recent decades, based on regularizing the local variational problem (Griffith criterion revisited). This original phase field damage model must satisfy the irreversibility condition of cracks, so a constrained variational inequality must be solved. Interest in this method within the mechanical community grew after the publication of Miehe et al., where the damage irreversibility condition is simplified through a history variable in the well-known PF-AT2 model. The damage is governed by this new variable, which prevents a decrease in the elastic potential. This simplification makes it possible to solve an unconstrained variational equality and consequently consider a simplified problem. For the PF-AT2 model, this simplification is consistent. Later, other phase field models (PF-AT1, PF-CZM, <span><math><mrow><mo>…</mo><mspace></mspace></mrow></math></span>) were developed, and the use of the history variable was adapted by other researchers to these newer models. In simulating structural damage with the phase field method, many authors have employed the simplified formulation involving the history variable. Therefore, this paper presents a critical comparison of the original (consider damage irreversibility condition) and the simplified (use history variable to approximate the damage irreversibility condition) phase field damage model, through many supported by extensive numerical tests.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"328 ","pages":"Article 111518"},"PeriodicalIF":5.3,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parameters affecting growth of local delaminations at transverse crack tips in [0m,90n]s cross-ply laminates","authors":"Anish Niranjan Kulkarni ,&nbsp;Andrejs Pupurs ,&nbsp;Janis Varna","doi":"10.1016/j.engfracmech.2025.111549","DOIUrl":"10.1016/j.engfracmech.2025.111549","url":null,"abstract":"<div><div>Transverse cracks in the 90-layers in cross-ply laminates have singular stress state at the crack tips. This causes formation of fiber/matrix debonds which coalesce into a local delamination along the 0/90-layer interface. Various studies in the literature have predicted onset strains for local delaminations at transverse crack tips using energy-based criteria such as critical strain energy release rate (ERR) and critical generalized stress intensity factors. Although similar ERR-based analyses have been carried out to predict the delamination growth as well, a systematic parametric analysis is lacking. Such systematic analysis of parameters that can affect the growth of local delaminations including geometrical parameters, elastic constants and transverse crack density is necessary to predict delamination growth under complex thermo-mechanical loading conditions. In the present work, FEM is used to carry out ERR-based analysis of the growth of local delaminations with different shapes in carbon-fiber epoxy and glass-fiber epoxy [0_m,90_n]s cross-ply laminates with the help of virtual crack closure technique and J-integral method. Firstly, the ratios of elastic constants and geometrical parameters that can prominently affect the ERR values are identified by a simple analytical routine. Then, the analytical predictions are verified using FEM for local delaminations growing symmetrically (I-shaped and C-shaped) or non-symmetrically (T-shaped and S-shaped) with respect to the laminate midplane. It is shown that a non-symmetrical I-shaped crack would always transition into a symmetrical I-shaped crack before any further delamination growth, if energetically viable. Finally, a simplified strategy to calculate ERR values for local delaminations growing under combined thermo-mechanical loading is presented.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"328 ","pages":"Article 111549"},"PeriodicalIF":5.3,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145105690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Characterization of cyclic visco-plastic behavior, damage and failure in high temperature weldments via an inverse method","authors":"Huijie Liu ,&nbsp;Ming Li ,&nbsp;Yan Wang ,&nbsp;Zhixun Wen ,&nbsp;Lu Cheng ,&nbsp;Xiufang Gong ,&nbsp;Zhufeng Yue ,&nbsp;Sean B. Leen ,&nbsp;Wei Sun","doi":"10.1016/j.engfracmech.2025.111548","DOIUrl":"10.1016/j.engfracmech.2025.111548","url":null,"abstract":"<div><div>High-temperature fatigue failures often occur in the heat-affected zone of welded joints, threatening the integrity of high-temperature piping components under flexible operation. This study presents an experimental–numerical framework for determining cyclic visco-plastic and damage properties, including the parent metal, weld metal, and heat-affected zone. A unified visco-plastic damage constitutive model is developed, coupled with high-temperature low cycle fatigue test for each of the constituents in the weldment. An analytical inverse approach is formulated to optimize the visco-plastic and damage properties of the parent metal and weld metal using high temperature uniaxial low-cycle fatigue tests data, while an FE-based inverse method is used to optimize HAZ properties via cross-weld fatigue test simulation. The framework is validated using cyclic test data from a P91 weldment, demonstrating the effectiveness of the FE-based inverse approach in characterizing full-life cyclic behavior and fatigue failure of the weldments.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"328 ","pages":"Article 111548"},"PeriodicalIF":5.3,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145105732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Review on specimen structure and bedding plane effects in mode-I fracture toughness testing of shale","authors":"Yu Suo ,&nbsp;Xianhang Wei ,&nbsp;Wei Cao ,&nbsp;ZheJun Pan ,&nbsp;Bing Hou ,&nbsp;Bin Huang ,&nbsp;Yuwei Li","doi":"10.1016/j.engfracmech.2025.111532","DOIUrl":"10.1016/j.engfracmech.2025.111532","url":null,"abstract":"<div><div>Fracture toughness (<span><math><msub><mi>K</mi><mrow><mi>I</mi><mi>C</mi></mrow></msub></math></span>) is a critical mechanical parameter for evaluating rock resistance to cracking and holds significant theoretical value for shale gas reservoir fracturing design and engineering stability assessment. To address key challenges in Mode-I fracture toughness testing of shale, this study consolidates International Society for Rock Mechanics (ISRM) and American Society for Testing and Materials (ASTM) standards with 118 recent global research findings to review five major specimen configurations (circular beam, short rod, disc, semi-circular disc, and transverse beam), analyzing their geometric design principles, <span><math><msub><mi>K</mi><mrow><mi>I</mi><mi>C</mi></mrow></msub></math></span> calculation frameworks, and bedding plane sensitivity characteristics. Research demonstrates: Chevron-Notched Circular Beams (CB) reduce pre-cracking errors but underestimate load by 18–22%; Straight-Notched Beams (SNB) show 30% <span><math><msub><mi>K</mi><mrow><mi>I</mi><mi>C</mi></mrow></msub></math></span> variation at &gt; 45° bedding angles. Short Rods (SR) exhibit 25% scatter at 30°. Disc specimens reveal: Cracked Chevron Notched Brazilian Disc (CCNBD) needs 3D stress correction; Cracked Straight Through Brazilian Disc (CSTBD) limits scatter to ≤ 8% despite &lt; 30% machining success; Hollow Center Cracked Disc (HCCD) optimizes crack paths; Hollow Double Wing Crack (HDWC) shows 60% <span><math><msub><mi>K</mi><mrow><mi>I</mi><mi>C</mi></mrow></msub></math></span> increase at 80 MPa with 10–15% error. Semi-circular Discs demonstrate 35% deviation in Notched Semi Circular Bend (NSCB) versus ≤ 10% in Cracked Chevron Notched Semi-Circular Bend (CCNSCB). Transverse Beams show Notched Deep Beam (NDB) overestimates <span><math><msub><mi>K</mi><mrow><mi>I</mi><mi>C</mi></mrow></msub></math></span> by 12–18%, while Chevron-Notched Deep Beam (CNDB) reduces variability by 15–20%. This research establishes fundamental theories and practical methodologies for precise fracture parameter measurement in shale fracturing, promotes the evolution of global testing standards, and facilitates the transition of rock fracture mechanics from laboratory research to field engineering implementation.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"328 ","pages":"Article 111532"},"PeriodicalIF":5.3,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145061052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Crack propagation of mixed mode I–II fracture in concrete under sustained loading","authors":"Maomao Yang ,&nbsp;Wei Dong ,&nbsp;Wenyan Yuan ,&nbsp;Binsheng Zhang ,&nbsp;Long Yu","doi":"10.1016/j.engfracmech.2025.111544","DOIUrl":"10.1016/j.engfracmech.2025.111544","url":null,"abstract":"<div><div>To investigate the crack propagation behavior of mixed mode I-II fracture in concrete under sustained loading, creep tests were conducted on concrete beams with five mode mixity ratios. The sustained load was maintained at 90% of the peak load. The digital image correlation technique was employed to monitor the crack propagation process. The results indicated that crack propagation process exhibited the three-stage feature: decelerated, uniform, and accelerated stages. As the mode mixity ratio decreased, the uniform stage duration increased, thereby enhancing the fracture lifetime. The logarithm relationship between the fracture lifetime and constant crack propagation rate was established, and a lifetime prediction method was validated for mixed mode I-II fracture under sustained loading. Additionally, the crack mouth opening displacement corresponding to the transition between the uniform and accelerated stages was closed to that at the peak load under static loading. The load-crack mouth opening displacement curve of mode I fracture under static loading was the envelope for that under sustained loading. Under static loading, the crack evolution is predominantly driven by the applied load, with crack growth and crack mouth opening occurring simultaneously; whereas under sustained loading, the crack evolution is governed by the time-dependent deformation. Due to the viscoelasticity of concrete, the crack propagation is delayed, while cracks continued to open. Notably, crack propagation path of mixed mode I-II fracture under sustained loading aligned well with that under static loading. These findings provide valuable insights into the crack propagation of mixed mode I-II fracture in concrete under sustained loading.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"328 ","pages":"Article 111544"},"PeriodicalIF":5.3,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145061051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"XFEM crack-tip enrichment using locally smoothed branch functions within blending elements","authors":"Tao Zheng,&nbsp;Gui-Yao Wang","doi":"10.1016/j.engfracmech.2025.111526","DOIUrl":"10.1016/j.engfracmech.2025.111526","url":null,"abstract":"<div><div>The Extended Finite Element Method (XFEM) is currently the mainstream numerical method for crack simulations in engineering. Its improvement, the Corrected XFEM, significantly enhances computational accuracy while introducing relatively severe ill-conditioned stiffness matrix issues. To address this, we investigate the spatial distribution of branch function-enriched terms describing the crack-tip singular displacement field in the XFEM displacement approximation. We note that the improvement of the Corrected XFEM essentially lies in adjusting the branch function-enriched displacement fields in the blending-element zone toward a specific smooth decay pattern. Based on this, we propose a simplified improvement method (the local smoothing method): within the standard XFEM framework, targeted scaling based on the enrichment status of nodes in the blending-element zone is applied exclusively to the branch functions in the same region. This scaling renders the function graph approximate a horizontal plane. Since the smoothing process solely employs scaling functions built upon element shape functions, its implementation into existing programs is straightforward. Numerical examples containing both crack-tip singular and non-singular fields demonstrate that compared to the Corrected XFEM, the proposed method exhibits comparable computational accuracy and a slightly higher convergence rate, along with significantly better numerical stability comparable to that of the standard XFEM.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"328 ","pages":"Article 111526"},"PeriodicalIF":5.3,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Tensile properties of three-dimensional stitched C/C composites prepared from different precursor materials at temperatures up to 2500 ℃","authors":"Xiaolong Li,&nbsp;Wenke Lu,&nbsp;Wangge Du,&nbsp;Yanfei Chen","doi":"10.1016/j.engfracmech.2025.111543","DOIUrl":"10.1016/j.engfracmech.2025.111543","url":null,"abstract":"<div><div>Three-dimensional stitched C/C composites are promising for ultra-high-temperature aerospace applications. This work investigates the tensile properties and failure mechanisms of C/C composites prepared from phenolic resin and coal tar pitch at temperatures up to 2500 °C. Results show that coal tar pitch-based C/C composites exhibit a tensile strength of 178.7 MPa at 2500 °C, higher than the resin-carbon-based composites. XRD illustrates that due to higher matrix graphitization in the former. As the temperature rises from room temperature to 2000 °C, the tensile strength of coal tar pitch-based composites increases from 191.4 MPa to 216.2 MPa, but decreases to 178.7 MPa at 2500 °C due to the accumulation of thermal residual stress. Large cracks and interface debonding are observed by SEM. Resin-carbon-based composites show minor tensile strength loss under different holding times. These findings provide insights into the use of C/C composites in thermal structures.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"328 ","pages":"Article 111543"},"PeriodicalIF":5.3,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145027388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mechanical mechanism of control holes in guiding the directional propagation of blast-induced cracks under in-situ stress conditions","authors":"Minghua Lin ,&nbsp;Wei Yang ,&nbsp;Ting Liu ,&nbsp;Baiquan Lin ,&nbsp;Tong Liu ,&nbsp;Yang Shen ,&nbsp;Xiangliang Zhang ,&nbsp;Shiqi Liu","doi":"10.1016/j.engfracmech.2025.111536","DOIUrl":"10.1016/j.engfracmech.2025.111536","url":null,"abstract":"<div><div>The rational design of control holes is crucial for achieving directional propagation of blast-induced cracks. Previous studies have overlooked the influence of the secondary stress field around the control holes on crack propagation. To address this issue, this study investigates the mechanical control mechanism by which control holes guide blast-induced cracks under in-situ stress conditions. Experimental results reveal that the guiding effect depends on the orientation of the in-situ stress conditions. Improper arrangement of control holes may lead to a secondary compressive stress field around them, which can inhibit crack propagation. Numerical simulations further show that when control holes are arranged in groups and the line connecting the blast hole and the control holes forms a 45° angle with the maximum and minimum principal stresses, the blast-induced cracks can effectively connect the control holes, achieving directional propagation.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"328 ","pages":"Article 111536"},"PeriodicalIF":5.3,"publicationDate":"2025-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fatigue crack propagation and life assessment of welded joints of corrugated web I-beams considering residual stress","authors":"Fulin Su ,&nbsp;Jiangning Pei ,&nbsp;Tielong Zhao ,&nbsp;Lijun Liu ,&nbsp;Bingbing Jin ,&nbsp;Shengbao Wang","doi":"10.1016/j.engfracmech.2025.111538","DOIUrl":"10.1016/j.engfracmech.2025.111538","url":null,"abstract":"<div><div>Corrugated web I-beams (CSWs) are widely used in bridge and construction engineering applications due to their lightweight, high strength, and superior buckling performance. Welding residual stress (WRS) has a significant impact on the fatigue performance of CSWs. However, its time-dependent behavior during crack propagation remains insufficiently studied. In this paper, the fatigue crack propagation mechanism and fatigue life evolution of CSWs welded joints are investigated through both experimental testing and numerical simulation. The specimens were fabricated using carbon dioxide gas shielded welding. Surface residual stresses on the flange plates were measured using the hole-drilling method, and a thermo-mechanical coupled finite element model was developed to validate the simulation accuracy. The results show that the simulated stresses agree well with the measured data. As the wave angle increases from 30° to 60°, the peak stress in the inclined flat region of the web increases from 159.9 MPa to 220.89 MPa, indicating more pronounced stress concentration. Crack propagation is dominated by the Mode I stress intensity factor (SIF), with the SIF at the deepest crack location being significantly higher than at the surface. A coupling relationship exists between crack geometry parameters, and an increase in the a/c ratio weakens the effect of twist angle on the SIF. The SIFs due to external loading and residual stress are independently calculated, and a residual stress relaxation mechanism is introduced to simulate stress redistribution during crack propagation. Residual stress significantly reduces fatigue life, and neglecting its influence leads to overestimation of fatigue life. Furthermore, ignoring the relaxation behavior during crack propagation amplifies prediction errors and causes substantial deviation from actual service conditions. The life assessment approach proposed in this study enhances prediction accuracy while maintaining computational efficiency and is applicable to the fatigue reliability analysis of complex welded structures.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"328 ","pages":"Article 111538"},"PeriodicalIF":5.3,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}