Mixed-mode Crack Research Articles

Numerical study of the influence of loading rate on fracture mechanism in elastoplastic rock-like materials with a modified phase-field model

The failure mode in rock engineering structures is closely related to the loading mode and loading rate, because of the inertial effects under a wide range of geological conditions. In this work, we propose a modified framework of the phase-field model coupled with plasticity, to investigate the effects of loading rates on the fracture mechanism in elastoplastic rock-like materials. By means of this framework, the damage-plasticity coupling effects on the mechanical responses and failure mode are also studied with an optimized pressure-sensitive plasticity model. The capability and accuracy of the proposed phase-field approach in capturing the nonlocal damage evolution is validated based on the elastic/inelastic homogeneous case with analytical solutions. Then the mixed-mode cracking behavior of the representative numerical examples are demonstrated under quasi-static and dynamic loading conditions from low to high loading rates. The failure modes, dynamic damage profiles and the crack propagation velocities in the examples with various loading rates were captured. Numerical results are discussed with comparison to previous experimental observations and available numerical works.

Multi-scale modelling of fatigue crack propagation due to liquid droplet impingement

We develop a sequential multi-scaling framework for studying the problem of fatigue crack propagation due to liquid droplet impingement. The scope is limited to a hypothetical material and a hypothetical liquid. The multi-scaling is achieved by handshaking the atomistic scale molecular dynamics (MD) simulations with the continuum scale smoothed particle hydrodynamics (SPH). The handshaking, in turn, is performed by evaluating the material, the fracture and the loading properties from MD simulations, and using them as inputs in the continuum scale SPH model. Due to the qualitative agreement of the pressure developed in the fluid and the substrate between the MD simulations and already published results, the liquid droplet impact in SPH is simulated through appropriate surface stresses. Further, we incorporate the pseudo-spring approach within the SPH model to develop a methodology for studying mixed-mode fatigue crack propagation. Our methodology provides good agreement with the existing literature for several cases. Lastly, we calculate the fatigue life of an edge-cracked specimen due to liquid droplet impingement.

The study of mixed mode fatigue crack growth mechanism of 25CrNiMo compact tensile specimens by experiment and finite element simulation

Fatigue cracking is the most common failure mode that endangers the safety and service life of parts. Initial manufacturing flaws are a critical factor affecting the growth of fatigue cracks. Currently, mixed-mode crack growth research frequently applies a simplistic two-dimensional finite element model, which cannot adequately represent the crack growth mechanism. An improved finite element method is proposed in this paper to overcome this drawback. Fatigue fracture propagation investigations on 25CrNiMo compact tensile specimens are conducted in this study, and the crack propagation rate is calculated using the Paris formula. Moreover, the special element modeling method and second-order Runge-Kutta integration method are utilized to perform finite element calculations on the 3D model. The results are highly consistent with the experimental test results. The propagation mechanism of cracks with varied initial inclination angles is explored depending on the finite element method. The relationship between the stress intensity measures KI, KII, and KIII is discovered to be competitive. The results have significant application value for the crack growth path prediction and crack life in parts with initial flaws.

Mixed-mode fatigue crack propagation simulation by means of [formula omitted] and walker models of the structural steel S355

In this paper, a numerical simulation method of mixed-mode fatigue crack propagation was explored using the extended finite element method (XFEM) and the Virtual Crack Closure Technique (VCCT). Both 2D and 3D numerical models were selected to simulate the fatigue crack propagation of steel specimens. Two coefficients were proposed to calculate the equivalent energy release rate (Geq) for a better simulation of the mixed-mode fatigue crack propagation of S355 steel. The Walker equation and the calculation formula of Geq were realized by a user-defined subroutine. A set of optimal correction coefficients of mode II energy release rate (GII) and mode III energy release rate (GIII) were quantitatively comparing the simulation results and test data. The results will contribute to fatigue crack propagation prediction of steel structures in the civil engineering field.

Forward and backward mixed-mode crack estimation using artificial neural network

PurposeIn this manuscript, the authors aimed to demonstrate the influences of influential parameters in mixed-mode crack propagation phenomenon. The authors attempted to cover almost all surrounding issues of this subject as the authors know simulating of propagating cracks as internal strong discontinuity is a complicated issue.Design/methodology/approachIn this manuscript, the authors demonstrated the influences of influential parameters in mixed-mode crack propagation phenomenon. The authors attempted to cover almost all surrounding issues of this subject as the authors know simulating of propagating cracks as internal strong discontinuity is a complicated issue. Furthermore, three different scenarios for crack growth are considered. In reality, edge-cracked plate, center-cracked plate and cracked plate in the presence of void and inclusion are studied. In fact, by designing suitable artificial neural network's (ANN) architectures all the three aforementioned conditions are trained and estimated through those architectures with very good agreement with input data. Also by conducting a series of sensitivity analysis, the most affecting factors in mixed-mode crack propagation in different situations are demonstrated. The obtained results are very interesting and useful for other researchers and also the authors hope the results would be cited by researchers.FindingsThe influential parameters on mixed-mode crack propagation were found in this paper.Originality/valueThe computer code using MATLAB was prepared to study the mixed-mode crack paths. Also using ANNs toolbox, the crack path estimation was investigated.

Experimental investigation on internal offset crack of PMMA beam using caustics

In this paper, the dynamic stress intensity factor (DSIF) at the crack tip of a PMMA beam containing an internal offset crack under impact loading was investigated by using a transmission digital caustic test system combined with high-speed camera. Firstly, the stress intensity factor, as well as velocity, of the mixed-mode crack tip under static and dynamic loading were derived based on the transmission caustic method; secondly, a drop hammer loading test was conducted on the different specimens with biased cracks in the beam using the transmission caustic test system to obtain the dynamic fracture mechanics parameters of internal crack initiation and expansion; then, the crack initiation angle and expansion path analysis of the impact-generated expansion cracks were performed based on the theoretical analysis and the differences between the fracture process and that of the specimens containing internal symmetric cracks were discussed. The results show that the different locations of the internal off-set cracks make the stress redistribution process inside the beam and the stress state at the crack tip during the crack extension process different, and the fracture process and fracture mechanics parameters are different from those of the specimens with internal symmetric cracks, the results of the caustic test are in good agreement with the numerical analysis. The research results can provide guidance for the study of the fracture process of brittle materials such as PMMA containing internal defects.

Investigation on the mixed mode fracture toughness of freshwater ice using the semi-circular bend method

The fracture toughness of ice is of great importance to understand the fracture behaviour of ice impact and blasting. In this study, the mixed mode (I + II) fracture toughness and mode II fracture toughness of granular freshwater ice were first investigated using the semi-circular bend method. A series of fracture tests were carried out to investigate the effects of the grain size (0.8 mm to 4.5 mm) and notch inclination angle (0° to 75°) on the fracture toughness under mixed mode loading conditions. The experimental results indicate that the mode II and mixed mode fracture toughness values slowly decrease in general as the grain size increases. The fracture initiation angles and critical stress intensity factors of the SCB ice specimens were predicted using the generalized maximum tangential stress (GMTS) criteria and conventional maximum tangential Stress (MTS). The GMTS criterion provides a better understanding for mixed mode fracture toughness of ice specimens with various grain sizes, particularly for mode II dominated loading conditions. The grain size of ice directly affects the size of the fracture process zone, which in turn affects the variation law of mixed mode fracture toughness. The strain field and displacement field were initially analysed based on digital image correlation. The results indicate that the variation in the mixed mode crack was complex, eventually exhibiting an asymmetrical distribution of the displacement field.

MIXED-MODE STRESS INTENSITY FACTOR EVALUATION BY INTERACTION INTEGRAL METHOD UNDER THERMAL AND MECHANICAL LOADS

The objective of this study is to present numerical aspects related to the implementation of the interaction integral method for the purpose of determining the stress intensity factors in mode I and mixed-mode crack problems of functionally graded materials (FGM) and homogenous materials for a different form of cracking. This numerical development is based on the use of the finite element method (FEM), by the coupling of the Ansys-Matlab calculation codes. To validate the accuracy and reliability of the approach, the results obtained will be compared with other numerical results in the literature. The interaction integral method is one of the methods most compatible with the formulation of the finite element method. Therefore, we are interested in this study, in terms of the presentation of necessary steps which allow the resolution of a problem by finite elements for the mechanical problems. It is very important to note that the principle of the implementation of the “Integral M” technique is using scripts based on the coupling of two commercial software.

Fatigue behavior and digital image correlation monitoring of steel plates with mixed-mode edge cracks repaired with CFRP materials

In recent years, carbon fiber reinforced polymer (CFRP) has been widely used to improve the fatigue behavior of steel structures, while most relevant studies were focused on steel components with mode I cracks. This study aims to investigate the fatigue behavior of steel plates with mixed-mode I/II edge cracks patched with CFRP sheets or plates. A total of eleven specimens were fabricated and tested. A digital image correlation (DIC) system was employed as a non-contact measurement to monitor the fatigue crack propagation. Post-processed displacement fields were used to calculate stress intensity factors (SIFs) near the crack tips. Experimental results showed that double-sided CFRP repairing could significantly improve the fatigue life of edge-cracked specimens, especially those with mode I crack rather than mixed-mode I/II crack. Corresponding finite element (FE) analyses were conducted, and good consistency was achieved with test results of crack growth trajectories and fatigue lives. Further FE analysis considered three parameters: load application angle, CFRP layer number, and initial damage level.

Bifurcation and propagation of mixed mode fatigue crack in steel plates repaired with prestressed CFRP laminates

The mixed-mode crack propagation model was proposed to predict crack growth trajectory of a central cracked tensile steel plate with prestressed carbon fiber-reinforced polymer (CFRP) reinforcement through verification of previous experiments. A sensitivity analysis of different parameters including CFRP fiber orientation, initial crack geometry, and prestress level was conducted to investigate CFRP repairing efficiency by using a combination of the programs FRANC3D and ABAQUS. The results show that the applied loading direction primarily governs the bifurcation angle of crack propagation. Increasing prestress level of CFRP along the applied loading direction can achieve ten-fold repairing efficiency of damaged steel structures.

Numerical simulation of rock erosion performance of a high-speed water jet using an immersed-body method

Water jet drilling (WJD) is an effective technique for drilling micro-holes in the subsurface for reservoir stimulation . This study aims to investigate numerically the failure mechanism of rock during WJD and to assess the WJD performance before drilling. A 3D fluid-solid coupling model is developed for simulating WJD by coupling a mechanical solver based on the combined finite-discrete element method (FDEM) with a fluid solver using an immersed-body method. The new numerical model is capable of simulating crack initiation and propagation and fragment removal under the impact load of a high-speed water jet. The poroelastic effect is implemented via Biot's theory of poroelasticity . The numerical results show that: (1) rock failure is only observed in the Gildehaus sandstone with the lowest strengths among the three types of rock tested, (2) most of the cracks are tensile failures and pure shear cracks are rare, mixed mode cracks account for 15%∼40% of the total crack number depending on the mechanical boundary conditions , (3) increased water back pressure significantly suppresses jet erosion. The poroelastic effect on the rock failure is insignificant in the mesoscale simulations and will be further investigated using a microscale model in future.

In-service failure of mechanically galvanised low alloy steel bolts of three 25,000 m3 bolted water tanks

Several single-lap bolted joints fastening the steel plates of three 25,000 m3 water tanks showed premature failure. Most fractured bolts were in the lower sector of the tanks.The tempered martensitic steel bolts were mechanically galvanised, and the poor quality of the galvanisation allowed the corroding agents (Cl− and SO4−2) to percolate through the Zn and Sn coating particles, finally reaching the steel surface of the bolts. Additionally, multiple 6 μm-deep intergranular pre-cracks were observed at the threads’ roots of the new bolts. During service, these pre-cracks accumulated the corrosive agents, creating numerous 10 μm-deep corrosion pits, nucleating the bolts’ environmentally assisted cracks. Microfractographic examination of the bolts featured stable growth of brittle cracks (intergranular and quasi-cleavage cracking) followed by mixed-mode cracking and a small region of ductile overload fracture. This failure sequence confirms that the fracture mechanism of the low alloy steel bolts is due to environmentally assisted cracking. Finite elements analysis investigated the effect of the bolt diameter, bolted joint design and pre-load force on the tensile stress distribution. Improvements in the bolts’ quality control and bolted joint design were discussed to prevent new failures.

Extended Powell–Sabin finite element scheme for linear elastic fracture mechanics

Powell–Sabin B-splines, which are based on triangles, are employed in the framework of the extended finite element method (XFEM) for fracture analysis. This avoids the necessity of remeshing in discrete fracture models and increases the solution accuracy around the crack tip. Powell–Sabin B-splines are C1-continuous throughout the whole domain. The stresses around crack tips are captured more accurately than when using elements with a standard Lagrangian interpolation. Although Powell–Sabin B-splines do not hold the Kronecker-delta property, the Heaviside function and the tip enrichment function are confined to the cracked elements only, similar to the traditional XFEM but different from the extended isogeometric method. In addition, Powell–Sabin B-splines still hold C1-continuous throughout cracked elements. There is no need to lower the continuity at element boundaries, to confine basis function support in cracked elements. Shifting is used to ensure compatibility with the surrounding discretization. The sub-triangle technique is employed for the numerical integration over crack elements. The versatility and accuracy of the approach to simulate crack problems are assessed in case studies, featuring mode-I and mixed-mode crack problems.

Experimental and numerical investigation of mixed-mode fatigue crack growth in nickel-based superalloy at high temperature

Fatigue cracking is one of the most common damage modes of aeroengine hot-end components, usually subjected to mixed-mode cracking. In this study, mixed-mode fatigue crack growth experiments at 550 °C are carried out using compact tension shear specimens made of nickel-based superalloy GH4169. Adaptive finite element method was used to verify several models at high temperature. The accuracy of angle dependent models was higher at 550 °C, and the rate of da/dN increased and decreased twice with crack propagating, which is different from room temperature (20–25 °C). This research could provide a basis for lifespan prediction of aeroengine hot-end components.

A new hybrid phase-field model for modeling mixed-mode cracking process in anisotropic plastic rock-like materials

Mixed-mode cracking is widely encountered in rock-like geomaterials under compression-controlled loadings. Some pending issues still need to be addressed. This work focuses on a new hybrid phase-field fracture method for cracking behavior of anisotropic plastic materials. Several new approaches are introduced. Firstly, a unified decomposition method of elastic strain energy driving crack growth is proposed by combining the advantages of classical spectral and volumetric–deviatoric decomposition algorithms. Then a new damage field evolution criterion is established, allowing to considering a nonlinear interaction between two basic crack propagation modes. The contribution of plastic strain energy to cracking process is investigated by considering an anisotropic yield criterion and combined isotropic-kinematic hardening laws. The validation of the established phase-field model is assessed by a series of representative examples, showing different types of cracking patterns. Sensitivity analysis of some key parameters involved in the model is also carried out to clarify the respective impacts on the progressive cracking patterns. Finally, the effectiveness of the proposed approach is validated by comparison with experimental results.

Investigation of the thermomechanical behavior of nonhomogeneous, layered materials with mixed-mode cracks subjected to rapid thermal shock loading

For mixed-mode, thermal shock crack problems with thermal lagging behaviors, it is difficult to obtain the transient thermal stress intensity factors (TSIFs). This paper aims to develop a method combining the Newmark method and the transient interaction energy integral method (IEIM) to extract the transient, mixed-mode TSIFs of nonhomogeneous, layered materials with mixed-mode cracks. The transient temperature field obtained by non-Fourier heat conduction theory is discretized in the spatial and temporal domains through the finite element method (FEM) and Newmark method, respectively. The effect of the continuity of thermomechanical parameters at the dual interface on the transient, mixed-mode TSIFs of nonhomogeneous, layered materials is discussed, then the fracture resistance of nonhomogeneous, layered materials is evaluated. Moreover, the maximum hoop stress criterion is utilized to obtain the crack growth angle and the equivalent, transient TSIFs of nonhomogeneous, layered materials. The influences of the interface on crack growth angle and equivalent transient TSIFs of nonhomogeneous layered materials are also studied. The present work is beneficial for the thermal design of nonhomogeneous, layered materials with mixed-mode cracks subjected to rapid thermal shock loading.

Controlling mixed-mode fatigue crack growth using deep reinforcement learning

Mechanical discontinuity embedded in a material determines the bulk mechanical, physical, and chemical properties. Under external forces, mechanical discontinuity undergo spatiotemporal propagation; thereby altering various properties of the material. This paper is a proof-of-concept development and deployment of a reinforcement learning framework, based on deep deterministic policy gradient, to precisely control both the direction and rate of the fatigue crack growth. The ability to control mechanical discontinuity in essence determines the key material properties. The desired control is relatively hard to achieve considering the large, continuous state and action spaces along with the exponential relationship between crack growth and stress cycle. The reinforcement-learning scheme is capable of learning an optimal and computational tractable control strategy. In the proposed approach, the reinforcement learning framework is integrated into an OpenAI-Gym-based environment that implements the mechanistic equations governing the fatigue crack growth. The learning agent does not explicitly know about the underlying physics, nonetheless, the learning agent can infer the control strategy by continuously interacting the numerical environment. The paper formulates an adaptive reward function involving reward shaping that can be generalized to similar control problems to improve the training efficiency. The reinforcement learning framework can successfully control the fatigue crack growth in a material despite the complexity of the propagation/growth pathway determined by multiple goal points. The paper provides the mathematical/physical basis of the reward function and the effect of neural network size and architecture and the state and action space that boosts the training speed while preserving the stability of the RL agents for the desired control problem.

Crack initiation characteristics of brittle materials with I‐II mixed mode crack under uniaxial compression

AbstractConsidering T‐stress components under compression, the crack initiation characteristics of HT200 and PMMA under uniaxial compression have been investigated by theoretical analysis and experimental study for central cracked plate (CCP) and compact tension shear (CTS) specimens with I‐II mixed mode crack. Crack initiation angles of CCP and CTS specimens under compressive load were theoretical predicted according to modified maximum tangential stress (MMTS) criterion and modified maximum shear stress (MMSS) criterion. The influence of material parameters and specimen geometrical configurations on crack initiation characteristics was illustrated through experiments. It demonstrates that the modified fracture criterion considering T‐stress components is more consistent with experiments. Crack initiation angle is related to material properties. Limit load PL is controlled by KII under compression for CCP specimen, and PL of PMMA is less than that of HT200. The closure effect on CTS specimens is less significant than that on CCP specimens.

Fatigue crack growth determination under in-phase and out-of-phase mixed-mode loading conditions using an automated DIC evaluation tool

In this study Digital Image Correlation (DIC) is utilized for measuring complex fatigue crack paths under spatial mixed-mode loading conditions. Therefore, an existing automated script was extended by two criteria for measuring the crack length versus the number of load cycles. Experimental investigations were conducted under mode I conditions, to calibrate the new evaluation routine. Moreover, in-phase and out-of-phase mixed-mode experiments under superimposed tension-torsion loading were performed to validate the method. The results show that the newly presented procedure provides an accurate, automated evaluation tool for mixed-mode fatigue crack growth tests, independent of the crack orientation and possible branching.

A three-field phase-field model for mixed-mode fracture in rock based on experimental determination of the mode II fracture toughness

In this contribution, a novel framework for simulating mixed-mode failure in rock is presented. Based on a hybrid phase-field model for mixed-mode fracture, separate phase-field variables are introduced for tensile (mode I) and shear (mode II) fracture. The resulting three-field problem features separate length scale parameters for mode I and mode II cracks. In contrast to the classic two-field mixed-mode approaches, it can thus account for different tensile and shear strength of rock. The two phase-field equations are implicitly coupled through the degradation of the material in the elastic equation, and the three fields are solved using a staggered iteration scheme. For its validation, the three-field model is calibrated for two types of rock, Solnhofen Limestone and Pfraundorfer Dolostone. To this end, double-edge notched Brazilian disk (DNBD) tests are performed to determine the mode II fracture toughness. The numerical results demonstrate that the proposed phase-field model is able to reproduce the different crack patterns observed in the DNBD tests. A final example of a uniaxial compression test on a rare drill core demonstrates that the proposed model is able to capture complex, 3D mixed-mode crack patterns when calibrated with the correct mode I and mode II fracture toughness.