Steady Crack Research Articles

On formulations for modeling pressurized cracks within phase-field methods for fracture

Over the past few decades, the phase-field method for fracture has seen widespread appeal due to the many benefits associated with its ability to regularize a sharp crack geometry. Along the way, several different models for including the effects of pressure loads on the crack faces have been developed. This work investigates the performance of these models and compares them to a relatively new formulation for incorporating crack-face pressure loads. It is shown how the new formulation can be obtained either by modifying the trial space in the traditional variational principle or by postulating a new functional that is dependent on the rates of the primary variables. The key differences between the new formulation and existing models for pressurized cracks in a phase-field setting are highlighted. Model-based simulations developed with discretized versions of the new formulation and existing models are then used to illustrate the advantages and differences. In order to analyze the results, a domain form of the J-integral is developed for diffuse cracks subjected to pressure loads. Results are presented for a one-dimensional cohesive crack, steady crack growth, and crack nucleation from a pressurized enclosure.

Low cycle fatigue response and fracture mechanism in a novel Al-3.5Si-0.5Mg-0.4Cu casting alloy

The LCF (low-cycle fatigue) behavior of a T6-treated low silicon cast aluminum alloy Al-3.5Si-0.5Mg-0.4Cu was investigated under axial symmetric tension-compression cyclic loading conditions. LCF behavior and results of experiment (under 6 different total strain amplitudes from 0.25 % to 0.5 %) are included. OM (Optical Microscopy), SEM (Scanning Electron Microscope), XRD (X-Ray Diffraction) and TEM (Transmission Electron Microscope) are employed to observe and analyze the fracture morphology and microstructure evolution. The results demonstrate that cracks were initiated from surface or subsurface defects. A higher total strain amplitude led to a smaller sum area of fatigue crack initiation region as well as a steady crack propagation regime, and a larger fatigue striation bandwidth. Furthermore, crack propagates along the interface between eutectic silicon and α-Al matrix under lower strain amplitudes. Otherwise, it extends through eutectic silicon particles if higher strain amplitudes are applied.

Measurement of Fatigue Crack Growth in Compact Tension Specimen Using an Optical Extensometer

Abstract In this investigation, fatigue crack growth (FCG) tests are performed on transformation induced plasticity steels to characterize the relevance of stress intensity and crack growth rates with standard compact tension (CT) specimens. An optical extensometer that can achieve real-time displacement measurement is developed based on digital image correlation. Instead of a displacement gauge, the optical extensometer is adopted in FCG tests to measure CT specimen crack opening displacement (COD). Compared with stress intensity, it is difficult to calculate crack growth rates with COD. Therefore, the compliance equation and incremental polynomial method are programmed with C++ languages to obtain the steady crack growth curve directly. The proposed method is verified with experimental results obtained by the displacement extensometer. In addition, the precision of the displacement measurement is assessed, and the error induced by displacement output rates is discussed.

Analytical and experimental investigation of the mode-II energy release rate of electrodes using a plasticity-assisted zero-degree peeling configuration

Lithium-ion batteries integrate heterogeneous materials such as active layers and current collectors, resulting in interfaces prone to delamination during the charge/discharge process. The mode-II energy release rate is a key index to evaluate the interfacial adhesion properties and structural integrity of electrodes. In this study, an analytical model considering the energy balance principle and a nonlinear constitutive model was established to characterize the mode-II energy release rate. A novel plasticity-assisted zero-degree peeling test (PAZDPT) is proposed to obtain a stable crack propagation stage where the peeling force is determined to calculate the mode-II energy release rate. Several parameter studies were conducted to verify the approximation of the stress distributions and simplification of the analytical model. The accuracy of the analytical model was validated against finite-element calculations. The results demonstrated an excellent agreement between the theoretical calculation and numerical results. Moreover, PAZDPT is conducive to steady crack propagation because it restricts the energy accumulation around the crack tip. The analytical model and newly proposed PAZDPT can also be extended to determine the mode-II energy release rate of other types of interfaces in bilayer thin-film materials.

Plane stress asymptotic solution for steady crack growth in an elastic/perfectly plastic solid for mode I crack propagation

Plane stress asymptotic solution for steady crack growth in an elastic/perfectly plastic solid for mode I crack propagation

Occurrence condition for steady crack propagation in quasi-brittle fracture and its application in determining initial fracture toughness

Crack propagation is commonly assumed to be a parallel motion called the steady state in quasi-brittle materials. The steady crack propagation can be used to determine softening traction-separation relation because one-to-one correspondence exists between the crack growth resistance and the softening traction-separation relation. However, the steady-state crack propagation that all quantities like crack opening displacement and cohesive stress keep invariable may not occur due to the limitation of the fracture process zone (FPZ). For quasi-brittle fracture, it is essential to define when the steady crack propagation occurs for ensuring the applicability to determine the softening traction-separation relation based on steady crack propagation. In this study, numerical test results of three specimen geometries, seven specimen sizes and three softening traction-separation relations are employed to analyze the steady crack propagation. Through comparison between crack growth resistance based on steady-state assumption and equivalent LEFM R-curve, a pseudo-steady state regime that is very similar to the steady crack propagation is found. At the pseudo-steady state, the relationship between the softening traction-separation relation and the crack growth resistance under steady crack growth is still applicable. The occurrence condition for the pseudo-steady crack propagation is deduced. It is found that for most laboratory specimens, the critical situation (load reaches its maximum value) can be seen as a pseudo-steady state with an error of <20%. By choosing the softening traction-separation relation based on the pseudo-steady assumption, the initial fracture toughness can be determined. The errors of the initial fracture toughness determined by this method can be approximately estimated based on the range of lFPZ/(D-ac).

Experimental investigation on the correlation between critical storage of elastic strain energy and crack extension in elastic–plastic materials

AbstractTo better solve the issues of steady crack extension with broad plasticity and the crack‐related problems in general yielding situations when the assumption of small‐scale plastic yielding fails, it is of great significance to further study the macroscopic mechanism of crack extension. In this paper, a new insight into the elastic–plastic crack extension is proposed on the foundation of critical storage of elastic strain energy (SESE). The feasibility of the new methodology is validated by designing and implementing two different experimental schemes in three typical elastic–plastic materials. The experimental results indicate that the critical SESE decreases linearly with the increase of crack length and U‐notch initial length. Besides, the SESE release rate is obtained through experimental and theoretical methods, and they are in the same order of magnitude and their value sequences are also accordant with all tested materials. Therefore, this investigation provides a new approach to characterizing crack extension in elastic–plastic materials.

Comparative study of the effects of different nanomaterials on the failure process of saturated concrete in an underground reservoir of a coal mine

The macroscopic failure of concrete used to form an artificial dam in an underground coal mine reservoir is the final manifestation of crack propagation and penetration: the mode of crack propagation is key to the safety evaluation of concrete structures. To improve the performance of concrete in such an artificial dam forming an underground coal mine reservoir, many scholars have investigated nano-modified concrete, but the effects of nanomaterials on the crack propagation mode and failure mode of saturated concrete are not yet fully understood. In the present research, uniaxial compression and acoustic emission (AE) experiments were conducted on saturated concrete specimens containing different types and amounts of nanomaterials, and the crack propagation mode, failure mode, and bearing capacity of different saturated concrete specimens were compared and studied. The results show that: the failure mode, crack propagation mode, and bearing capacity of saturated concrete can be modified by adding nanomaterials, and the type and content thereof can affect the modification effect provided. Considering the strength, bearing capacity, and crack-propagation mode, saturated concrete specimens containing 3 wt% nano-Al2O3 exhibit the best performance, with characteristics of high strength, high bearing capacity, steady crack propagation, and small-scale cracking. The results have guiding significance for damage-warning and safety assessment of hydraulic structures.

Competing effects of current density and viscoplastic deformation on the critical conditions for dendrite growth into solid-state lithium battery electrolytes

All-solid-state lithium (Li) batteries provide a promising pathway toward high energy and power density. Dendrite penetration through the solid electrolyte causing battery short-circuit, however, persists to be one of the challenges impeding their widespread application. Here, considering a pre-existing surface crack in the electrolyte initially filled with an infinitely thin layer of Li, and assuming Li deposit to behave in accordance with rigid-viscoplasticity, we seek for the steady state Li-filled crack opening profile that could potentially form at a given constant current density. Treating the chemical potential of Li ions in the electrolyte and the electric potential to be uniform along the crack face, the model accounts for the coupling between stress buildup in the dendrite, deposition rate, viscoplastic flow of Li deposit, and crack opening induced by electrolyte deformation using singular integral equations of fracture mechanics. The model establishes limiting conditions for crack growth before a steady state dendrite is reached, triggering a cycle of crack growth and dendrite elongation. Using material properties adopted from literature, the model predicts that the critical condition can be met for a microcrack at typical current densities. The effect of pressure applied to the cell is further discussed.

Transient and steady state viscoelastic crack propagation in a double cantilever beam specimen

Crack growth in viscoelastic materials is understood with the use of cohesive models, or steady state theories which focus on viscoelastic dissipation. We consider a double cantilever beam (DCB) specimen under a remote constant pure moment, which is initially suddenly applied to the beams. It is shown that the response to the applied moment rapidly reaches a steady state in terms of crack propagation speed. In contrast, it is shown that the external work rate, contributing to fracture energy, stored elastic energy and viscous dissipation, has a transient that possibly lasts a significantly longer time. The dissipation rate increases with speed for a standard material, reaching a limit governed by the ratio of instantaneous to relaxed modulus. However, the initial dissipation rate at low crack propagation speeds can be orders of magnitude larger than the latter limit, and depends on the ratio between the initial crack size and the fracture process zone size, a regime which we define ultratough. For thin beams, we do not find any evidence, even in the steady state, of the dissipation-based theories’ suggestion of a reduced maximum load and then of an unstable regime of decreasing load with speed.

A comparison of uniaxial and multiaxial non-proportional fatigue properties in cast Al-Si-Cu-T6 alloys solidified at two cooling rates: Fatigue behavior, fracture characteristics and dislocation evolution

The cyclic deformation behavior and fatigue fracture characteristics of cast Al-Si-Cu-T6 (A319-T6) alloys solidified at two cooling rates under uniaxial and multiaxial non-proportional loading conditions were investigated. The A319-T6 alloy exhibited cyclic hardening and additional non-proportional hardening effects during cyclic loading. The cyclic hardening rate and non-proportional loading sensitivity coefficient improved by 2.8% and 5.1%, respectively, when the solidification cooling rate was increased from 0.1 to 10 °C/s. To account for the hardening effects, the dislocation evolution and interaction between dislocations and other microstructures were analyzed. Based on the asymmetry parameter, the tension-compression symmetries of A319-T6 alloys subjected to uniaxial and multiaxial non-proportional loading were discussed. The presence or absence of a steady crack propagation area was considered to be the primary difference in the cross-section caused by cooling rates, leading to varied fracture flatness. Multiaxial non-proportional loading yielded reciprocating wear marks and a significant quantity of wear debris on the fracture surface. The majority of wear debris was identified as matrix oxide. The reciprocating wear process removed fatigue striation and secondary cracks that emerged on the uniaxial fracture, further increasing fracture flatness.

Plastic anisotropy and twin distributions near the fatigue crack tip of textured Mg alloys from in situ synchrotron X-ray diffraction measurements and multiscale mechanics modeling

In spite of many potential applications due to their superior mechanical properties, magnesium alloys still find many practical restrictions primarily due to our limited knowledge of their failure mechanisms. In situ and non-destructive strain measurements on the microstructural scales are critical in understanding the fatigue crack behavior, which has greater advantages than the macroscopic measurements based on replica technique and the small-scale mechanical testing that cannot easily provide a complete view on the synergy of many scale-dependent deformation and failure mechanisms. This work exploits the state-of-the-art synchrotron X-ray diffraction technique to attain in situ strain mapping results, with high spatial resolution, near a fatigue crack tip in the highly textured ZK60 Mg alloy. The accurate measurements in the plastic zone are compared to a micromechanical modeling framework, in which the steady fatigue crack is simulated by an irreversible, hysteretic cohesive interface model and the surrounding plasticity by Hill anisotropic plasticity. The general agreement in the anisotropic deformation fields is reached down to half of the plastic zone size towards the crack tip, while the discrepancy right at the crack tip can be used to develop an inverse model to extract the material-specific fatigue damage evolution in our future work. It is surprisingly noted that twin activities are localized in a narrow band from the tip to the wake of the fatigue crack, irrespective of the crack growth direction of this textured alloy. Such twin-crack interactions are understood here by our crystal plasticity finite element simulations with several representative crystallographic orientations.

Time-Frequency Characteristics of Acoustic Emission Signals on Water-Bearing Sandstone Specimen Subjected to Conventional Uniaxial Compression

This paper presents an experimental investigation of acoustic emission (AE) time-frequency characteristics of a water-bearing sandstone specimen in a conventional uniaxial compression test. The main achievements are as follows: (1) The violent fluctuation of AE time domain parameters indicates that the water-bearing sandstone specimen is about to be destroyed. This characteristic provides a theoretical basis for predicting the failure of water-bearing rock in engineering practice. (2) In the elastic phase, the AE b value is the lowest but has a sudden increase after falling into the steady crack propagation phase. In the unsteady crack propagation phase, the AE b value is further increased. This characteristic is of great indicative value for predicting the failure of the water-bearing sandstone specimen. (3) The difference of dominant frequency among the three key points is very small, indicating that the crack initiation and propagation of the water-bearing sandstone specimen has a certain stability in the damage and failure process. But, the two-dimensional frequency spectrum structure of AE waveform signals shows that the closer to failure, the more the number of the frequency spectrum structure peaks. (4) The energy of AE signals is mainly concentrated in the first three frequency bands. The closer to failure, the more the energy proportion of the first three frequency bands is reduced; conversely, the energy proportion of the latter five frequency bands is increased, which leads to more complexity of the failure modes of the water-bearing sandstone specimen.

Mechanical behaviors and failure criteria of seawater sea-sand engineered cementitious composites under combined tension and shear

Seawater sea-sand engineered cementitious composites (SS-ECC) is promising for alleviating both the shortage of freshwater and river sand and the brittleness caused by replacing steel bars with fiber reinforced plastic/polymer (FRP) bars. However, the mechanical properties of SS-ECC at complicated stress state are not systemically investigated, and the corresponding failure criteria are not established. This study experimentally investigated the mechanical properties of SS-ECC under various combined tension-shear loads by a specially designed test fixture. The results showed that SS-ECC under combined tension and shear presents multiple cracking and micro-cracks with the crack width of no more than 0.24 mm. The load-displacement curves of SS-ECC are divided into elastic stage, steady cracking stage and failure stage. When loading angle increases from 10° to 70°, crack number and maximum resultant force decrease due to increasing number of fiber rupture. Compared with control group, SS-ECC under combined tension and shear exhibits excellent strength and ductility. Finally, through analysis based on the generalized twin shear stress strength theory, the failure law of SS-ECC under the combined loading is well described.

Experimental investigation on Mode I crack growth and damage mechanism of sandstone subjected to cyclic loading

To further investigate the Mode I crack growth and damage mechanism, compression tests were performed on notched semi-circular bending (NSCB) specimens at different cycle amplitudes. The crack propagation gauge and digital image correlation (DIC) recorded the entire process of crack growth. The real-time crack growth rate and evolution of the horizontal strain field during crack growth were obtained. Based on the crack growth rate, the crack growth process can be divided into three stages: the cracking latent period (primary stage), stable crack growth stage (secondary stage), and accelerated crack growth stage (tertiary stage). The cracking latent period accounts for a large proportion of the entire crack growth. The stable crack (i.e., steady subcritical crack growth) expanded slowly to a certain extent after initiation, and then the accelerated crack growth led to failure. With the increase in the cyclic amplitude, the cracking latent period is shortened and the crack growth rate is accelerated. The crack growth rate is positively correlated with the stress intensity factor. Moreover, scanning electron microscopy (SEM) was used to analyse the development of the fracture process zone (FPZ) and the subcritical crack damage mechanism. The SEM images showed two damage phenomena: (1) intergranular cracks caused by grain debonding (primary mechanism) and (2) transgranular cracks (secondary mechanism).

Rock dynamic fracture of a novel semi-circular-disk specimen

The relationship between velocity, acceleration, and dynamic fracture toughness during rapid crack propagation is difficult to effectively capture. In this study, a novel semi-circular holed disc bend is proposed to achieve a long fracture path. Hopkinson pressure rods with crack growth and strain gauges are used to impact the semi-circular holed disc bend specimens and to monitor the cracking process of a mode-I fracture. The experiments show that the crack growth speed increases to a critical value after crack initiation and then oscillates as a result of the reflected stress wave. The dynamic propagation fracture toughness ( K IC d ) increases with increasing crack velocity for steady crack propagation; however, this does not apply for unsteady propagation. An experimental–numerical–analytical method is developed to determine the dynamic stress intensity factor , which initially increases with time, then decreases, and ultimately increases again. The acceleration ( v ˙ ) can be used to investigate the unsteady crack propagation process. K IC d values for v ˙ < 0 are greater than those for v ˙ > 0. An energy release rate formula related to v ˙ and the crack propagation velocity ( v ) is proposed and verified by the experiments. A thorough understanding of v , v ˙ , and K IC d is important to analyze high-speed fault rupture processes.

Delamination properties and in situ damage monitoring of z-pinned carbon fiber/epoxy composites

Abstract Carbon-fiber-reinforced composites with layer stacking structures are sensitive to delamination crack. To improve the interlaminar properties and further explore the capability of in situ damage monitoring of the laminate, CCF300 and CCF800 carbon fiber pins were selected to fabricate the z-pinned composites. Compared with the control sample, the G IC values of CCF300 and CCF800 z-pinned composites are increased by 398 and 378%, respectively. This indicates that the delamination resistance improvement of the laminates is dominated by the z-pin debonding and pull-outs. The electrical resistance of the laminates was utilized to in situ monitor the crack propagation within the composite laminate. The results show that the presence of the z-pins enhances the sensitivity of damage detection. The ΔR/R 0 of CCF800 z-pinned composite is nearly three times that of the control sample at the moment the crack length reaches 110 mm. Crack length–displacement curves were obtained according to the relationship between ΔR and Δa, which clearly displayed the steady or stick-slip crack growth of the laminates with or without z-pins, respectively. Visualization of the crack growth process can provide a novel method for the delamination failure analysis of the composite.

Shear fracture performance of the interface between ultra-high toughness cementitious composites and reactive powder concrete

This study used unnotched compression tests and digital image correlation technology to analyze the influence of two different casting intervals and three different roughness conditions on the fracture toughness of the interfaces between ultra-high toughness cementitious composite (UHTCC) and reactive powder concrete (RPC). UHTCC exhibits pseudo-strain-hardening responses and multi-cracking behaviors, and the most notable characteristic of RPC is its dense microstructure. The results show that the complete interfacial shear fracture process included three stages: crack initiation, steady crack propagation and unsteady crack propagation. A double-K crack propagation criterion for interfacial shear fracture of composite structures was proposed by introducing two parameters: initial and unstable fracture toughness. After introducing interfacial roughness via the scratch method, the unstable fracture toughness decreased. The 24-h casting interval group had a lower initial fracture toughness and higher unstable fracture toughness than the 2-h group. The unstable fracture toughness of all the composite specimens exceeded that of C60 concrete, indicating that they had excellent resistance to interfacial shear fracture.

A peridynamic model for fracture analysis of polycrystalline BCC-Fe associated with molecular dynamics simulation

In this work, based on the traction-separation (T-S) constitutive relations extracted from molecular dynamics (MD) simulation, a peridynamics (PD) model is proposed to investigate the crack propagation behavior of the polycrystal BBC-Fe under mode I loading condition. MD simulation is carried out to give an insight into the cracking process and fracture mechanism according to the analysis of atomic configuration and stress distribution. The atomic stress at the crack tip with respect to the opening distance is tracked during the steady cracking stage to provide a stable T-S relation. The fracture parameters of single crystal Fe are obtained via MD simulation, based on which the PD parameters are obtained through an energy equivalent method. After that, a PD approach combined with cohesive zone model (CZM) is proposed to study the mode I fracture in polycrystal Fe. A good agreement has been found between the proposed PD model and the classical CZM based on a quasi-static splitting test of a single Fe crystal. Subsequently, PD simulations are performed concerning the dynamic crack propagation in a polycrystal Fe. What’s more, the effect of grain size, the grain boundary strength and the horizon size of PD on the fracture characteristics are examined. It can be concluded that the T-S relation originated from classical cohesive theory can be regarded as an effective bridge between MD and PD. This work provides a new thought to study the fracture behavior of polycrystals from the atomic deformation mechanism to micro-fracture description.

Computational and fractographic study of the stable growth of low cycle fatigue cracks in the disk of an aircraft engine turbine under complex loading cycles

The results of a comprehensive computational and experimental study of the kinetics of low-cycle fatigue cracks (LCF) in a turbine disk made of EP741NP granular nickel alloy of an aircraft gas turbine engine under complex loading cycles (CLC) are presented. The configuration of crack fronts was reconstructed using light microscopy. Steps of the blocks of fatigue striations characterizing the crack increment under CLC at the stage of steady crack growth are measured using scanning electron microscopy during microfractographic analysis. The period of LCF crack steady growth is estimated and the reproducibility of the regularities of steady growth is demonstrated which testifies the capability of reliable prediction for LCF crack steady growth. The finite element modeling of the reconstructed crack fronts has been carried out. The values?? of the range of stress intensity factor at each crack front in the area of measuring the pitch of the striation blocks were calculated for the subcycles of complex loading cycles. Using the previously developed physically grounded mathematical model and calculation methodology, forecasting of stable growth of the LCF crack was carried out. The results of forecasting match the data of micro-fractographic analysis unlike the results of LCF crack growth prediction based on Paris law which differ significantly from experimental data.