Three-dimensional Crack Propagation Research Articles

A thermodynamic framework for ductile phase-field fracture and gradient-enhanced crystal plasticity

This study addresses ductile fracture of single grains in metals by modeling of the formation and propagation of transgranular cracks. A proposed model integrates gradient-extended hardening, phase-field modeling for fracture, and crystal plasticity. It is presented in a thermodynamical framework in large deformation kinematics and accounts for damage irreversibility. A micromorphic approach for variationally and thermodynamically consistent damage irreversibility is adopted. The main objective of this work is to analyze the capability of the proposed model to describe transgranular crack propagation. Further, the micromorphic approach for damage irreversibility is evaluated in the context of the presented ductile phase-field model. This is done by analyzing the impact of gradient-enhanced hardening considering micro-free and micro-hard boundary conditions, studying the effect of the micromorphic regularization parameter, evaluating the performance of the model in ratcheting loading and testing its capability to predict three-dimensional crack propagation. In order to solve the fully coupled global and local equation systems, a staggered solution scheme that extends to the local level is presented.

Crack propagation and damage evolution of metallic cylindrical shells under internal explosive loading

This paper investigates the three-dimensional crack propagation and damage evolution process of metallic column shells under internal explosive loading. The calibration of four typical failure parameters for 40CrMnSiB steel was conducted through experiments and subsequently applied to simulations. The numerical simulation results employing the four failure criteria were compared with the differences and similarities observed in freeze-recovery tests and ultra-high-speed tests. This analysis addressed the critical issue of determining failure criteria for the fracture of a metal shell under internal explosive loads. Building upon this foundation, the damage parameter Dc, linked to the cumulative crack density, was defined based on the evolution characteristics of a substantial number of cracks. The relationship between the damage parameter and crack velocity over time was established, and the influence of the internal central pressure on the damage parameter and crack velocity was investigated. Variations in the fracture modes were found under different failure criteria, with the principal strain failure criterion proving to be the most effective for simulating 3D crack propagation in a pure shear fracture mode. Through statistical analysis of the shell penetration fracture radius data, it was determined that the fracture radius remained essentially constant during the crack evolution process and could be considered a constant. The propagation velocity of axial cracks ranged between 5300 m/s and 12600 m/s, surpassing the Rayleigh wave velocity of the shell material and decreasing linearly with time. The increase in shell damage exhibited an initial rapid phase, followed by deceleration, demonstrating accelerated damage during the propagation stage of the blast wave and decelerated damage after the arrival of the rarefaction wave. This study provides an effective approach for investigating crack propagation and damage evolution. The derived crack propagation and damage evolution law serves as a valuable reference for the development of crack velocity theory and the construction of shell damage evolution modes.

Study on the effect of three-dimensional crack initiation and propagation and plastic zone of crack front on fracture-splitting quality of connecting rod

Study on the effect of three-dimensional crack initiation and propagation and plastic zone of crack front on fracture-splitting quality of connecting rod

Research on the influence of rock fracture toughness of layered formations on the hydraulic fracture propagation at the initial stage

Deep underground rocks exhibit significant layered heterogeneity due to geological evolution and sedimentation. Rock fracture toughness, as one of the important indicators of hydraulic crack propagation, also exhibits heterogeneous distribution. In order to investigate the influence of non-uniform fracture toughness of layered rocks on hydraulic crack propagation, this paper establishes a planar three-dimensional hydraulic crack propagation model. The model is numerically solved using the 3D displacement discontinuity method (3D-DDM) and the finite difference method. The calculation results indicate that when the distribution of the fracture toughness of layered rocks changes from uniform to non-uniform, the fracture morphology develops from a standard circular crack to an elliptical crack. When the difference of the rock fracture toughness between adjacent rock layers and the middle rock layer (pay zone) is large enough, the fracture morphology will develop towards a rectangular shape. In addition, when the fracture toughness of rock layers is non-uniformly distributed, the hydraulic crack not only rapidly expand in the softening layer (rock layer with lower fracture toughness), but also slowly propagate in the strong layer (rock layer with higher fracture toughness). However, the propagation speed in the softening layer is much faster than that in the strong layer. The results indicate that the heterogeneity of rock fracture toughness has an important impact on the morphology, propagation speed, and direction of hydraulic fractures.

Research on influence mechanism of prefabricated hole on life extension of compressor impeller

The life of compressor impeller is very short under extreme working conditions, so it is necessary to explore the life extension method and mechanism. Since the crack initiation location cannot be accurately predicted in advance, the hole drilling strategy of prefabricated hole will determine the remaining life of impeller after cracks appear. This article presents a strategy of prefabricated hole to extend the fatigue crack propagation life (FCPL) of compressor impeller. The stress distribution of impeller during operation is simulated by finite element method, and the crack initiation location is determined. The Forman-Newman-de Koning model is used to investigate the effects of hole drilling strategy and rotational speed on FCPL, and the three-dimensional crack propagation process is simulated. In addition, this paper investigates the main phenomena and influencing mechanism for the extension of FCPL due to prefabricated hole. It is found that the prefabricated hole can attract the crack propagation path, and make the crack pass through the hole more easily. At this time, the crack propagation driving force will decrease sharply, and the crack propagation rate will decrease accordingly, thus extends the FCPL. Even if it cannot pass through the hole, the optimal hole drilling strategy can extend life by 104.23%. The life extension effect of prefabricated hole increases with the increase of speed. The design in this paper can reduce the economic cost to a great extent, and provides a new idea for the life extension problem of complex models.

Thermal corrosion fatigue crack growth behavior and life prediction of 304SS pipeline structures in high temperature pressurized water

The influence of transient water temperature changes on the fatigue crack growth behavior of 304SS pipeline structures was studied based on high-throughput testing method through the modification of dual loop circulating water equipment. Results demonstrated that the fatigue crack growth rate gradually decreased with the decrease of cooling rate, and the crack growth rate was exponentially related to the cooling rate. Both the base material and weld of the stepped pipe showed a transgranular cracking mode, and propagated continuously by slip-oxidation mechanism. Compared with the fine equiaxed grain of the base material, the grain in the weld was coarse and the residual strain was large, and the crack growth rate of the weld was obviously higher. Then, the thermal fatigue crack growth rate model for stepped pipes was established by combining finite element thermo-mechanical coupling simulation and three-dimensional crack propagation analysis software, and the model was modified based on the experimental results.

A dynamic damage constitutive model and three-dimensional internal crack propagation of rock-like materials in bond-based peridynamic

The original bond-based peridynamic model addresses brittle fracture rather than progressive fracture. It also does not account for the impact of strain rate on bond strength and fails to incorporate the impact of internal length on non-local long-range forces. As a result, it is inadequate for simulating the dynamic failure of rock-like materials under impact loading. To address these limitations, a new approach involves a sextic polynomial attenuation function. This function captures the impact of internal length on non-local long-range forces and leads to the derivation of a corresponding micro-modulus expression. A damage function and a new failure criterion are integrated to describe the nonlinear mechanical behavior and progressive failure of rock-like materials. The influence of strain rate on bond dynamic strength is considered to reflect the strain rate effect in rock materials. The outcome is a newly proposed dynamic damage constitutive model that overcomes the three shortcomings of the original bond-based peridynamic model when simulating the dynamic failure of rock-like materials. Numerical examples are simulated based on this model, and their results are compared with the experimental data. This comparison allows further exploration of the volumetric fracturing behavior and mechanical properties of rock specimens with internal flaws in three dimensions when subjected to impact loading. The findings demonstrate the effectiveness of the proposed model in accurately simulating crack propagation and mechanical properties across varying strain rates in rock-like materials. Notably, the internal flaw's depth significantly influences the specimen's mechanical properties and energy utilization efficiency at a specific flaw angle α=90°. Complex three-dimensional cracks, consisting of shell-like, wing, anti-wing, and shear cracks, emerge due to the interconnection of various crack types. The shape of these cracks is intricately linked to the flaw angle and depth. Ultimately, this model solves the challenge of capturing internal crack growth during dynamic impact processes that are often difficult to observe in experimental tests.

Study of fatigue fracture characteristics for duplex stainless steel STHE welded joint specimen

A shell and tube heat exchanger (STHE) welded joint is considered for fatigue fracture mechanism. The joint is made up of a protruding tube fabricated to a tubesheet by means of welding. A super duplex stainless steel (DSS) material is used for the tube and tubesheet. Fatigue test was newly conducted using the single tube test specimen. The initial cracking plane was moved from the minimum sectional-area plane that was perpendicular to the loading direction, and the crack growth was almost planar. Stress analysis is carried out using finite element method (FEM) and the stress distributions are carefully studied by comparing the simple perforated plate. In addition, three-dimensional crack propagation (CP) simulation is performed employing extended finite element method (X-FEM). Fracture phenomenon is verified using the experimental and numerical crack front geometries. The fracture mechanics parameter is evaluated and verified with empirical formulae. CP behaviors are carefully discussed based on the fracture mechanics parameter. The CP life is presented for three loading amplitudes. The FAT class of the STHE welded joint is studied based on the available design standards such as BS, IIW and JSSC. Finally, the fatigue fracture characteristics of the STHE welded joint specimen are shown through the experimental and numerical methods.

Experimental study on the effect of different shear reinforcement shapes and arrangement on 3D crack propagation and shear failure mechanism in RC beams

Surface crack patterns have been considered to determine the shear failure behavior of RC beams but the effect of three-dimensional crack propagation on shear crack development and shear strength of RC beams is still debatable. In this study, a three-dimensional crack evaluation was carried out to investigate the shear failure mechanism of RC beams with different shapes and arrangement of shear reinforcement (close shape shear reinforcement, rod shape reinforcement with mechanical anchorage, combination of close shape reinforcement and rod shape reinforcement, rod shape reinforcement and transverse distribution rebar) using three-point loading test by keeping the amount of shear reinforcement same in all beams. The load displacement relationships, 3D crack maps, stirrup strain and concrete strain relationships with displacement and shear resistance components were discussed in detail and these information’s are useful for designing and shear strengthening of existing beams. It was clarified that a clear difference in three-dimensional cracking pattern, shear resistance components of concrete and shear reinforcement contribution was observed in RC beams. This was due to the shear reinforcement shapes and arrangement of rod shape reinforcement, which influenced the shear strength of RC beams.

Numerical simulation of 3D fracture propagation problem with reproducing kernel peridynamic method

The non-ordinary state-based peridynamic (NOSB-PD) method has significant advantages in solving crack propagation problems due to its non-local characteristics, but it also faces problems such as numerical oscillations and boundary effects. In order to solve the above defects, the paper first discusses the NOSB-PD method within the Galerkin framework. After that, the peridynamic differential operator (PDDO) approximation was introduced by extending the calculation of the deformation gradient tensor F in NOSB-PD. Since the zero-order approximations in the PDDO approximation and the reproducing kernel (RK) approximation are identical, the distinctions between the two approximations have been thoroughly analysed. Although the two approximations show the same consistency, only the RK approximation satisfies the integrable condition. Therefore, a RK-PD coupling method is proposed in the paper, and an implicit iterative algorithm suited to the RK-PD method is presented as well. At last, several numerical examples demonstrate that the proposed method does not suffer from numerical oscillations and can be used to solve the three-dimensional crack propagation problems.

A moment quadrature method for uncertainty quantification of three-dimensional crack propagation via extremely few model runs

The finite element-based three-dimensional crack propagation analysis has increasingly been used in many design assessment applications, particularly those high reliability-demanding structures subject to complex multi-axial fatigue loading. Such analysis is computationally intensive and poses a great challenge to current uncertainty quantification methods, which normally require a substantial number of finite element model runs. This study proposes a new method for uncertainty quantification of finite element-based three-dimensional crack propagation analysis under material uncertainty via extremely few, normally 2d, model runs, and d is the number of uncertain variables. When the classical two-parameter Paris’ equation is employed as the fatigue crack growth rate model, a total number of 4 model runs are sufficient. The method employs the Hankel matrix of moments associated with the uncertainty variables to determine the optimal nodes and weights in the variable space for Gauss quadrature under prescribed distributions. A two-step time integration scheme is employed to further reduce the number of propagation steps within an individual finite element model run. The accuracy of the proposed method is validated using a practical case with realistic fatigue testing data and analytical solutions. The holistic method is applied to two three-dimensional crack propagation problems to demonstrate the effectiveness. It is shown that using 4 model runs the mean and variance of the crack front can be accurately captured under material uncertainty.

Three-Dimension Crack Propagation Behavior of Conical-Cylindrical Shell

The conical-cylindrical shell is prone to stress concentration in the convex cone position under the action of deep-sea pressures. This results in unidirectional or bidirectional positive tensile stresses on the surfaces of the shell. The conical-cylindrical shell is a large, welded structure. Welding residual stress was generated at the cone-column joint position, resulting in high-stress concentration at this location. Under both the residual stress of welding and seawater pressure, cracks easily form and propagate on the shell weld toe, leading to fatigue damage and even structural failure. In this paper, based on the seawater’s alternating load and the residual stress of welding, the three-dimensional crack propagation process was studied for the submarine conical-cylindrical shell. The effects of crack depth and shape ratio on crack propagation trend and fatigue life were analyzed. The results can provide references for predicting the crack propagation trend, assessing the remaining life and evaluating the structural safety of the submarine conical-cylindrical shell.

Field-enriched finite element method for simulating of three-dimensional crack propagation

Field-enriched finite element method for simulating of three-dimensional crack propagation

Improved XFEM (IXFEM): 3D dynamic crack propagation under impact loading

An improved XFEM (IXFEM) for three-dimensional non-planar crack propagation under impact loadings is developed. The proposed method couples the IXFEM (Tian and Wen, 2015; Wen and Tian, 2016) and the B-spline ruled surface method (BRSM) proposed previously by authors (Xiao, Wen and Tian (2021)). The issues of the standard XFEM for dynamic crack propagation, such as energy inconsistency, “null” critical time step size and optimal mass lumping at crack tip, are fundamentally avoided with an extra-DOF free PU approximation (Tian, 2013). The tip singularity enrichment is introduced to assure high accuracy through the extra-DOF free PU approximation. The BRSM, which is designed to solve the challenge about robust and efficient geometry representation of 3D non-planar surface crack growth, is applied to model the geometry of the 3D dynamic crack propagation in this paper. The interaction integral for 2D dynamic stress intensity factor (SIF) evaluation is extended to 3D. Efficiency of the proposed approach is demonstrated via numerical tests.

Experimental study on mechanical properties and failure characteristics of sandstone containing a pre-existing surface flaw under dynamic loading

Dynamic loading tests were conducted on sandstone specimens containing a three-dimensional surface flaw with different angles and depths using a modified split Hopkinson pressure bar (SHPB) device. A high-speed camera with digital image correlation method was used to record the crack initiation, propagation and failure process of specimens and to monitor the surface strain field. The test results show that both the angle and depth of the surface flaw have an important influence on the dynamic mechanical properties and energy dissipation of the specimens. The specimen is least weakened at a surface flaw angle of 90°, with the angle having a greater effect on dynamic strength and energy absorption at greater depths. Analysis of the x-axis direction strain, shear strain and y-axis direction strain fields by DIC shows that the crack initiation is due to a combination of tensile and shear stresses. Both the angle and depth of the surface flaw have a significant effect on the failure patterns. Specimens show shear failure at surface flaw angles less than or equal to 60° and tensile failure at surface flaw angles of 75° and 90°. When the angle of surface flaw is less than or equal to 60°, there are more shear cracks at greater depths. The complexity of three-dimensional crack propagation under dynamic loading was confirmed by the observation of traces of internal shell-like crack growth in a partial fragmentation of specimen after failure.

Experimental and Numerical Study on the Anchorage Effect of Bolted Jointed Rock Masses

Anchor technology has become an irreplaceable geotechnical engineering reinforcement measure. To clarify anchorage effects and investigate the three-dimensional (3D) crack propagation process of bolted jointed rock masses, a series of physical model tests and 3D numerical simulations were performed, and optimal anchoring conditions of jointed rock masses are found. The results showed that a bolted jointed rock mass had stronger compressive performance and deformation capability, with crack propagation controlled, especially in the anchorage zone, and the formation and slip of shear zones also restrained. Meanwhile, the fractured location is transferred from the joint tip to the interface between the bolt and surrounding rock. The numerical simulation based on the damage model of rocks at the mesoscale and a nonlinear shearing–sliding model for anchoring interfaces were conducted with the FLAC3D code to reproduce the 3D crack propagation and the gradual damage of bolted jointed rock masses. The anchorage effect increased the crack initiation stress of jointed rock masses, but the zone where the bolt passed through the joint cracked more easily. Once onset of the instability stage of the bolted jointed rock mass, cracks began to propagate and penetrate gradually to the anchorage zone. In addition, under uniaxial compression, a “Z”-shaped shear stress concentration zone is observed in the bolt, which is mainly attributed to the role of the bolt on controlling shear failure along the joint plane and transverse dilatancy of the specimen. Better anchorage effects were achieved by installing bolts after deformation of the jointed rock mass had developed to a certain extent. The optimal anchor opportunity for a jointed rock mass varied with the joint angle. More specifically, for the rock mass with a joint angle of 75°, the anchorage effect was best when the bolt was installed at 40% peak strain of the jointed rock mass, while 10% peak strain was perfect for the bolted rock mass with a 45° joint angle.

Dynamic modeling of the gear-rotor systems with spatial propagation crack and complicated foundation structure

Considering both spatial crack fault and complex foundation structure, the dynamic finite element model and multi-body dynamic model are established simultaneously to analyze the dynamic characteristics of gear-rotor systems. Firstly, the extended finite element method is used to simulate the three-dimensional crack propagation paths of spur gears under partial load. Then, based on the proposed three-dimensional loaded tooth contact analysis (3D-LTCA) method, the mesh stiffness of spur gears with the spatial crack and complex foundation is calculated and the results are verified by the finite element method. Finally, the dynamic finite element model and multi-body dynamic model of the gear-rotor system are established. The dynamic responses under different crack levels are analyzed. The advantages and disadvantages of these two dynamic models are evaluated. According to the above analysis, it is indicated that the 3D-LTCA can accurately consider the influence of complex foundation and spatial crack on mesh stiffness. The finite element model and multi-body dynamic model can effectively analyze the influence of crack fault and foundation structure on dynamic responses.

An X-FEM based framework for 3D fatigue crack growth using a B-spline crack geometry description

This paper presents an X-FEM based iterative framework for numerical simulation of three-dimensional fatigue crack propagation. To accurately describe the crack geometry, B-spline curves and surfaces are used for the crack front and faces respectively. A new crack front extension method based on the Möller–Trumbore algorithm is introduced to achieve fully automated crack growth for complex geometries. To validate the presented work, three different cases are discussed: (1) compact tension specimens with an asymmetrically located hole, (2) a beam with a slanted crack subjected to a three-point bending load and (3) a beam with a slanted crack subjected to a torsion load. Good agreement between the numerical and experimental results is observed.

Three-dimensional fatigue crack propagation by means of first order SIF approximation

In this paper we make use of a closed-form solution for mode I Stress Intensity Factors (SIF) in three-dimensional planar flaws based on homotopy transformations of a disc. The utilised equations are very accurate when the flaw is a small deviation from a circle. Under the hypothesis of an isolated crack, the SIF at each point of the crack border is calculated to assess the crack shape after propagation. The solution is proposed in terms of the Fourier series and the crack growth rate equation is taken according to Paris’ low. Many examples are proposed with the aim of predicting the final shape of different types of embedded planar flaws in butt welded joints under fatigue tensile loading.

Internal 3D cracks evolution and the toughening mechanisms of the hierarchical structures in Strombus gigas shell

Strombus gigas shell is a lightweight, high-strength and high-toughness biocomposite material. In-depth exploration of its internal microstructure characteristics and the corresponding strengthening and toughening mechanism is of great significance to the design of high-performance composite materials. Here, the high-resolution synchrotron radiation X-ray computed tomography technology was adopted to carry out the in-situ three-dimensional investigation on the deformation and fracture evolution of the internal crossed-lamellar hierarchical structures of the Strombus gigas shell during the tensile process. In the experiment, some important three-dimensional crack initiation and propagation evolution phenomena were observed, such as the multi-point bursting, progressive propagation and spatial network arrangement of cracks and the reverse ‘C’-shaped cracks, which may have great contribution to the load-bearing capacity and toughness of the shell. According to the mechanical analysis of the visualized evolutionary information of the deformation and fracture of hierarchical microstructures, a strengthening and toughening regulation mechanisms that driven by the local stress concentration, and guided by the hierarchical structure and weak interface was proposed. This study may have a positive guiding significance for exploring and learning the toughening design strategy of lightweight composites.