Crack Tip Deformation Research Articles

Short rolling contact fatigue and thermal cracks under frictional rolling – A comparison through simulations

The relative severity of radial (thermal) and inclined rolling contact fatigue surface cracks of equal depth in a railway wheel is investigated by three-dimensional elastoplastic finite element analyses of a cracked wheel sector subjected to contact loading. Response is quantified by relative displacements of nodes close to crack tip and at the crack mouth. Highly inclined cracks give the highest magnitudes of crack tip shear displacements, which is the dominant deformation mode. Braking conditions are found to open the crack mouth. Initially higher temperatures on thermal cracks cause increased crack tip deformation and opening of the crack, whereafter subsequent mechanical load cycles impose crack closure.

Experimental validation of relationship between fracture parameters J and CTOD for SE(B) and SE(T) specimens during ductile crack growth

In structural assessments, the crack driving force is usually estimated numerically based on the \(J\)-Integral definition because its determination is well established in many finite element codes. The nuclear industry has extensive fracture toughness data expressed in terms of \(J\)-Integral and huge experience with its applications and limitations. On the other hand, the material fracture toughness is typically measured by CTOD parameter using the plastic hinge model or double-clip gauge technique. The parameter CTOD has a wide acceptance in the Oil and Gas Industry (OGI). Also, the OGI has a lot of past data expressed in terms of CTOD, and the people involved are very familiar with this parameter. Furthermore, CTOD parameter is based on the physical deformation of the crack faces and can be visualized and understood in an easy way. There is a unique relationship between \(J\) and CTOD beyond the validity limits of linear elastic fracture mechanics for stationary cracks. However, if ductile crack propagation happens, the crack tip deformation profile and stress–strain fields ahead of the crack tip will change significantly when compared to the static case. Thus, the stable crack propagation may change the well-established relationship between \(J\) and CTOD for stationary cracks compromising the construction of resistance curves \(J\)-\(\Delta a\) from CTOD-\(\Delta a\) data or vice versa. A search in the open literature was undertaken to get experimental measurements of \(J\)-Integral and CTOD data including ductile crack growth. Then, using theoretical relations developed in previous work, predictions for CTOD values from \(J\) values are performed and directly compared with the experimental values. The present results provide additional understanding of the effects of ductile crack growth on the relationship between \(J\)-Integral and CTOD for standard fracture specimens. Specific procedures for the evaluation of CTOD-R curves using SE(T) and SE(B) specimens are proposed.

Microstructure-Scale In-Situ Image Correlation-Based Study of Grain Deformation and Crack Tip Displacements in Al–Cu Alloys

Abstract Mechanistic understanding based on experimental measurements of grain and crack tip deformation at relevant length scales is critical for improvement of physics-based modeling of microstructurally-sensitive fatigue crack propagation and for the computationally-assisted design of more durable materials. In this study, single-crystal, bi-crystal, and large-grain multi-crystal specimens of Al–Cu alloys are fabricated, characterized using electron backscattered diffraction (EBSD), and mechanically tested. In addition to conventional optic al–imaging based 3D image correlation (IC), scanning electron microscope (SEM) based high-resolution 2D IC is used to measure displacements within grain interiors, near crack tips, and grain boundaries. The use of micro-scale IC and EBSD-based experiments is discussed as they relate to the development of crystal-plasticity-based finite element models (CP–FEMs). This article specifically highlights experimental methods that have been developed to obtain the relevant data needed for CP–FEM calibration and validation.

Discrete dislocation modeling on interaction between type-I blunt crack and cylindrical void in single crystals

The interaction between a type-I blunt crack and a near-tip void were modeled by the two-dimensional discrete dislocation dynamics (2-D DDD), with special emphasis on the void growth, crack-tip deformation and their size effect. Different from the classical crystal plasticity-based FE modeling, the present 2-D DDD modeling clearly indicates that, even for the type-I opening crack, the horizontal slip bands connecting the crack tip and the void surface are easily formed, especially when the ligament between the crack-tip and void surface is not too long. Besides the horizontal slip bands, some asymmetric slip bands which are at an oblique angle to the horizontal x-axis can also be formed and intersect with the micro-void. On two coupled parallel slip bands, some oppositely signed dislocations, which can be regarded as equivalent prismatic dislocation loops, glide toward the void/crack-tip surface and thus drive the void growth and the crack tip further blunting. In addition, the size effect by ligament length and void radius on void growth and crack-void interaction has also been investigated carefully. It was found that the size effect is closely related to the formation of horizontal shear slip bands. There exists a critical void radius, under which the near-tip void tends to change into a flat shape and its area decreases gradually with increasing the applied stress intensity factor (SIF) K. These results might be helpful for a better understanding of the fracture and damage mechanisms in the crack-tip process zone.

J-dominance and size requirements in strength-mismatched fracture specimens with weld centerline cracks

The strong dependence of crack-tip fields on specimen geometry and remote loading, particularly for moderate-to-low hardening materials under LSY conditions underlies the constraint loss phenomenon and invalidates the one-parameter characterization of unstable cracking behavior in terms of the \(J\)-integral. Previous research efforts have enabled establishing size requirements for valid \(J\) fracture toughness testing based on the dominance of the HRR singularity which are essentially applicable to homogeneous materials. Only little effort has been expended in the past years to extend the one-parameter characterization of crack-tip conditions to welded structural components. The present work addresses the coupling effect of specimen geometry and weld strength mismatch on the crack-tip deformation limits for which \(J\)-dominance is valid in weld centerline fracture specimens. Very detailed nonlinear finite element analyses of plane-strain models for common specimen geometries, including deep and shallow crack bend SE(B) and tension SE(T) fracture specimens, with weld centerline cracks enable resolving the required crack-tip stress fields from which the variation of crack-tip constraint with increased values of \(J\) can be assessed. The present study provides further insight into the coupled effects of specimen geometry and weld strength mismatch on the levels of deformation limit defined by \(M=(b\sigma _{0}^{WM})/J\), where \(b\) is the remaining crack ligament and \(\sigma _{0}^{WM}\) denotes a reference (yield) stress for the weld material, at which a one-parameter characterization of crack-tip stress fields still remains valid.

The role of grain boundary structure and crystal orientation on crack growth asymmetry in aluminum

Atomistic simulations have shown that the grain boundary (GB) structure affects a number of physical, mechanical, thermal, and chemical properties, which can have a profound effect on macroscopic properties of polycrystalline materials. The research objective herein is to use atomistic simulations to explore the role that GB structure and the adjacent crystallographic orientations have on the directional asymmetry of an intergranular crack (i.e. cleavage behavior is favored along one direction, while ductile behavior along the other direction of the interface) for aluminum grain boundaries. Simulation results from seven 〈110〉 symmetric tilt grain boundaries (STGBs) show that the GB structure and the associated free volume directly influence the stress–strain response, crack growth rate, and crack tip plasticity mechanisms for middle-tension (M(T)) crack propagation specimens. In particular, the structural units present within the GB promote whether a dislocation or twinning-based mechanism operates at the crack tip during intergranular fracture along certain GBs (e.g., the ‘E’ structural unit promotes twinning at the crack tip in Al). Furthermore, the crystallography of the adjacent grains, and therefore the available slip planes, can significantly affect the crack growth rates in both directions of the crack – this creates a strong directional asymmetry in the crack growth rate in the Σ 11 (113) and the Σ 27 (552) STGBs. Upon comparing these results with the theoretical Rice criterion, it was found that certain GBs in this study ( Σ 9 (221), Σ 11 (332) and Σ 33 (441)) show an absence of directional asymmetry in the observed crack growth behavior, in conflict with the Rice criterion. The significance of the present research is that it provides a physical basis for the role of GB character and crystallographic orientation on intergranular crack tip deformation behavior.

Improved extended digital image correlation for crack tip deformation measurement

The objective is to find an appropriate shape function which can enhance the performance of Extended Digital Image Correlation (X-DIC). This paper presents an improved X-DIC methodology to measure the discontinuous deformation across the crack. After simplifying the shape function of crack tip element based on the linear elastic fracture mechanics, non-rectangular subset is proposed to eliminate the effect of the crack width on the measurement accuracy. Then, the work verifies the performance of improved X-DIC by measuring the deformation of a specimen with a mode I crack. Experimental results show that the proposed method is effective at improving the measurement accuracy and enhancing the computational efficiency of X-DIC. In the end, the thesis provides a practical application of improved X-DIC to crack tip deformation measurement.

Fracture behavior of epoxy nanocomposites modified with polyol diluent and amino-functionalized multi-walled carbon nanotubes: A loading rate study

The synergistic effects of reactive polyol diluent and amino-functionalized multi-walled carbon nanotubes on fracture of two- and three-phase (hybrid) epoxy nanocomposites are investigated under quasi-static and dynamic loading conditions. Digital image correlation method with a drop-tower and high-speed camera are used for dynamic tests. The crack-tip deformation histories and fracture parameters for stationary and growing cracks are extracted. Tests show improved crack initiation toughness in modified-epoxies relative to the neat resin with the highest enhancement in hybrid nanocomposites. The dynamic crack initiation toughness values are found to be consistently lower than the static counterparts. Fractographic examinations reveal distinct rate-dependent morphologies.

The Research on Oblique Crack Tip Deformation Field of Airship Envelope Composites Based on the Digital Speckle Correlation Method

The tearing mechanical properties and the deformation field distribution of 45 degree oblique direction of the crack tip was studied on the stratospheric airship envelope reinforced by plain woven Kevlar-fiber composite. Here, the material samples were prefabricated with the initial length of 20mm unilateral incision, and the digital speckle correlation experimental method was used to obtain the perpendicular crack tip displacement and strain fields with artificial spots under mono-axial tear test. The results show the deformation field changes with the characteristic of discrete step and the strain concentration phenomenon, and the strain concentration zone expands as increasing tensile load. The warp and weft step maximum displacement reaches 6.00mm and 1.7mm, and deformation in every step exhibits a diminishing step law, the warp deformation in the rear area of the crack tip are evenly, while the shear and weft strain volatile in a wide range

Application of Reddy's third-order theory to delaminated orthotropic composite plates

In this work the third-order shear deformation theory by Reddy is applied and modified to analyze delaminated orthotropic composite plates . The delaminated plate portion is captured by Reddy's traditional theory, while a novel double-plate system is developed for the undelaminated part. It is shown that in the uncracked part four conditions are required to satisfy in symmetrically delaminated plates. The conditions involve the imposition of traction-free boundaries and the interface constraints. These four conditions enable the reduction of the parameters from nine to five in the displacement field. The governing equations show significant coupling among the stress resultants of the uncracked portion, that has to be considered in the continuity conditions between the delaminated and undelaminated parts. To demonstrate the application of the present model a simply-supported delaminated plate subjected to a concentrated force is analyzed. The distribution of the mode-II and mode-III energy release rates and their ratio are calculated using the 3-dimensional J -integral. The finite element model of the plate is also created using brick-type elements. The comparison of the analytical and finite element results shows very good agreement. It is shown that the deformations around the delamination front can be captured by the third-order plate theory with high accuracy. • We derive the governing equations of modified Reddy's theory. • The displacement field is based on the interface constraints. • The delamination causes sudden changes in the strains and stresses. • Third-order plate theory is required to capture the crack tip deformations.

Comparison of Concurrent Multiscale Methods in the Application of Fracture in Nickel

This paper presents a study of fracture in nickel using multiscale modeling. A comparison of six concurrent multiscale methods was performed in their application to a common problem using a common framework in order to evaluate each method relative to each other. Each method was compared in both a quasi-static case of crack tip deformation as well as a dynamic case in the study of crack growth. Each method was compared to the fully atomistic model with similarities and differences between the methods noted and reasons for these provided. The results showed a distinct difference between direct and handshake coupling methods. In general, for the quasi-static case, the direct coupling methods took longer to run compared to the handshake coupling methods but had less error with respect to displacement and energy. In the dynamic case, the handshake methods took longer to run, but had reduced error most notably when wave dissipation at the atomistic/continuum region was an issue. Comparing each method under common conditions showed that many similarities exist between each method that may be hidden by their original formulation. The comparison also showed the dependency on the application as well as the simulation techniques used in determining the performance of each method.

The microstructure and fracture performance of styrene–butadiene–methylmethacrylate block copolymer-modified epoxy polymers

The microstructure and fracture performance of an anhydride-cured epoxy polymer modified with two poly(styrene)-b-1,4-poly(butadiene)-b-poly(methyl methacrylate) (SBM) block copolymers were investigated in bulk form, and when used as the matrix material in carbon fibre reinforced composites. The ‘E21’ SBM block copolymer has a higher butadiene content and molecular weight than the ‘E41’. A network of aggregated spherical micelles was observed for the E21 SBM modified epoxy, which became increasingly interconnected as the SBM content was increased. A steady increase in the fracture energy was measured with increasing E21 content, from 96 to 511 J/m2 for 15 wt% of E21. Well-dispersed ‘raspberry’-like SBM particles, with a sphere-on-sphere morphology of a poly(styrene) core covered with poly(butadiene) particles, in an epoxy matrix were obtained for loadings up to 7.5 wt% of E41 SBM. This changed to a partially phase-inverted structure at higher E41 contents, accompanied by a significant jump in the measured fracture energy to 1032 J/m2 at 15 wt% of E41. The glass transition temperatures remained unchanged with the addition of SBM, indicating a complete phase separation. Electron microscopy and cross polarised transmission optical microscopy revealed localised shear band yielding, debonding and void growth as the main toughening mechanisms. Significant improvements in fracture energy were not observed in the fibre composites, indicating poor toughness transfer from the bulk to the composite. The fibre bridging observed for the unmodified epoxy matrix was reduced due to better fibre–matrix adhesion. The size of the crack tip deformation zone in the composites was restricted by the fibres, hence reducing the measured fracture energy compared to the bulk for the toughest matrix materials.

A Multi-resolution Experimental Methodology for Fatigue Mechanism Verification of Physics-based Prognostics


 
 
 An experimental methodology is proposed in this paper for mechanism verification of physics-based prognosis of mechanical damage, such as fatigue. The proposed experimental methodology includes multi-resolution in-situ mechanical testing, advanced imaging analysis, and mechanism analysis based on digital measurements. A case study is presented for fatigue crack growth mechanism investigation. In-situ fatigue testing at lower resolutions, i.e., optical microscopy, and digital image correlation is used to analyze the plastic deformation behavior and strain distribution near crack tips. In-situ fatigue testing under higher resolutions, i.e., scanning electron microscopy, and automatic image tracking is used to obtain detailed crack tip deformation and crack growth kinetics at the nanometer scales. Following this, the proposed experimental methodology is applied to two different metallic materials, aluminum alloys and steels. Very different experimental observations are observed and the underlying mechanisms are discussed in detail. The impact on the prognosis algorithm development is also discussed. Finally, the potential application of the proposed experimental methodology to other materials systems and to other types of mechanical damage is discussed.
 
 

A nonlinear symmetry breaking effect in shear cracks

Shear cracks propagation is a basic dynamical process that mediates interfacial failure. We develop a general weakly nonlinear elastic theory of shear cracks and show that these experience tensile-mode crack tip deformation, including possibly opening displacements, in agreement with Stephenson's prediction. We quantify this nonlinear symmetry breaking effect, under two-dimensional deformation conditions, by an explicit inequality in terms of the first and second order elastic constants in the quasi-static regime and by semi-analytic calculations in the fully dynamic regime. Our general results are applied to various materials. Finally, we discuss related works in the literature and note the potential relevance of elastic nonlinearities for various problem, including frictional sliding.

A constraint-equivalent approach for assessing fracture toughness of RPV steels under neutron irradiation

Neutron irradiation damages reactor pressure vessel (RPV) steels. As a result of material degradation, the mechanical properties of the material are changed and the crack tip stress and deformation fields are altered. The reduction of fracture toughness due to neutron irradiation is shown to be equivalent to a “constraint shift” exhibited by the ductile–brittle transition curve. Using the J–A2 two-parameter fracture theory to quantify the crack tip stress field and a critical crack opening stress as the fracture criterion, the fracture toughness of an irradiated RPV steel can be predicted from its nonirradiated value. The procedure and examples are given in the paper.

Speed-dependent tip fields of a moving crack in a hyperelastic material

This paper gives an asymptotic analysis of plane strain deformation and stress fields near the tip of a steady moving crack in a compressible hyperelastic material. The semi-infinite crack is assumed to be in an infinite homogeneous harmonic material under a constant remote mode-I loading. The crack tip deformation and stress fields are derived up to the third order, which ensures the strict positivity of the Jacobian determinant in the vicinity of the moving crack tip. The derived solutions are applied to a specific hyperelastic material for which some recent experimental data are available in the literature. The comparison with the experimental data showed that the crack-face profile and the energy release rate predicted by the present model are in reasonable agreement with experiments and several recent finite-strain elastic models. In addition, the crack branching angle predicted by the present model also agrees well with some known experimental data. All of these results suggest that the harmonic material model has the potential to capture the main features of finite deformation phenomena in the dynamic fracture of hyperelastic materials.

Role of inclusion stiffness and interfacial strength on dynamic matrix crack growth: An experimental study

Experimental simulations of dynamic crack growth past inclusions of two different elastic moduli, stiff (glass) and compliant (polyurethane) relative to the matrix (epoxy), are carried out in a 2D setting. Full-field surface deformations are mapped in the crack–inclusion vicinity optically. The crack growth behavior as a function of inclusion–matrix interfacial strength and the inclusion location relative to the crack is studied under stress-wave loading conditions. An ultra high-speed rotating mirror-type digital camera is used to record random speckle patterns in the crack–inclusion vicinity to quantify in-plane displacement fields. The crack-tip deformation histories from the time of impact until complete fracture are mapped and fracture parameters are extracted. The crack front is arrested by the symmetrically located compliant inclusion for about half the duration needed for complete fracture event. The dynamically propagating crack is attracted and trapped by the weakly bonded inclusion interface for both stiff and compliant symmetrically located inclusion cases, whereas it is deflected away by the strongly bonded stiff inclusion and attracted by strongly bonded compliant inclusion when located eccentrically. The crack is arrested by a strongly bonded compliant inclusion for a significant fraction of the total dynamic event and is longer than the one for the weakly bonded counterpart. The compliant inclusion cases show higher fracture toughness than the stiff inclusion cases. Measured crack-tip mode-mixities correlate well with the observed crack attraction and repulsion mechanisms. Macroscopic examination of fracture surfaces reveals much higher surface roughness and ruggedness after crack–inclusion interaction for compliant inclusion than the stiff one. Implications of these observations on the dynamic fracture behavior of micron size A-glass and polyamide (PA6) particle filled epoxy is demonstrated. Filled-epoxy with 3% Vf of PA6 filler is shown to produce the same dynamic fracture toughness enhancement as the one due to 10% Vf glass.

Ratchetting strain as a driving force for fatigue crack growth

Ratchetting deformation has significant implications on material damage and fatigue life of components under service loading conditions. In this work, we explore the concept of ratchetting strain as a driving force in controlling crack growth, both time-independent and time-dependent, utilising elasto-plastic, visco-plastic and crystal-plasticity constitutive models. Characteristics of crack tip deformation were examined for both stationary and growing cracks using the finite element method. Whilst the strain range and the stress range remained largely unchanged throughout the loading cycles, distinctive strain ratchetting behaviour near the crack tip occurred in all cases, leading to progressive accumulation of tensile strain normal to the crack growth plane. It seems plausible that this tensile strain, or ratchetting strain, may be responsible for material separation leading to crack growth. The effects of material constitutive model, grain orientation and loading frequency on the development of ratchetting strain were also examined. Ratchetting strain was found to be related to accumulated plastic strain; and both were used in a crack growth criterion with which the crack growth rates of a nickel alloy were predicted. The preliminary results seem to be encouraging.

Microscale characterization of granular deformation near a crack tip

This paper presents a study of microscale plastic deformation at the crack tip and the effect of microstructure feature on the local deformation of aluminum specimen during fracture test. Three-point bending test of aluminum specimen was conducted inside a scanning electron microscopy (SEM) imaging system. The crack tip deformation was measured in situ utilizing SEM imaging capabilities and the digital image correlation (DIC) full-field deformation measurement technique. The microstructure feature at the crack tip was examined to understand its effect on the local deformation fields. Microscale pattern that was suitable for the DIC technique was generated on the specimen surface using sputter coating through a copper mesh before the fracture test. A series of SEM images of the specimen surface were acquired using in situ backscattered electronic imaging (BEI) mode during the test. The DIC technique was then applied to these SEM images to calculate the full-field deformation around the crack tip. The grain orientation map at the same location was obtained from electron backscattered diffraction (EBSD), which was superimposed on a DIC strain map to study the relationship between the microstructure feature and the evolution of plastic deformation at the crack tip. This approach enables to track the initiation and evolution of plastic deformation in grains adjacent to the crack tip. Furthermore, bifurcation of the crack due to intragranular and intergranular crack growth was observed. There was also localization of strain along a grain boundary ahead of and parallel to the crack after the maximum load was reached, which was a characteristic of Dugdale–Barenblatt strip-yield zone. Thus, it appears that there is a mixture of effects in the fracture process zone at the crack tip where the weaker aspects of the grain boundary controls the growth of the crack and the more ductile aspects of the grains themselves dissipate the energy and the corresponding strain level available for these processes through plastic work.

Numerical and experimental analyses of the plasticity-induced fatigue crack growth in high-strength steels

Numerical analyses of plasticity-induced fatigue crack growth (FCG) were performed for high-strength steels. FCG proceeds by large crack tip deformations promoting transfer of material from the tip apex to the crack flanks, thus rendering plastic crack growth based on plastic deformations without bond breaking or material splitting at the crack tip (Laird–Smith mechanism of FCG by blunting and re-sharpening). Plastic FCG rates (d a/d N) p were obtained and numerical results were fitted with a Paris-like equation (d a/d N) p = CΔ K m . An experimental validation of the simulations was performed by comparing the numerical Paris-like equation with real (experimental) Paris equations in the steels.