Crack Tip Displacement Fields Research Articles

Automatic crack tip localization in enormous DIC images to in-situ characterize high-temperature fatigue crack growth behavior

Digital Image Correlation (DIC), with its advantages of full-field, non-contact and applicability to extreme environments, is a powerful deformation measurement technique to in-situ monitor the high-temperature fatigue crack propagation behavior. For the DIC-based fracture mechanics analyses of cracking, crack tip position in DIC images, which is usually determined visually and manually, plays a significant role. However, the long-term fatigue-DIC experiment at both room-and high-temperatures poses a real challenge due to the huge amount of DIC images, lower image quality at high-temperature, and even the invisibility of cracks. In this paper, a fully automated algorithm for localizing the crack tip is proposed based on the crack tip displacement field and the immune algorithm. Compared to traditional algorithms, it does not necessitate iterative initial values of crack tip location, and permits precise and fast determination of critical fracture mechanics parameters, such as the Stress Intensity Factors (SIFs). The algorithm reliability is validated by both numerical simulation and fatigue testing of nickel-based superalloy GH4169 at room temperature and 650℃. It is shown that crack tip position and SIF values can be precisely and automatically determined within 7 s per image using an ordinary low-cost computer, which significantly improves the analyzing efficiency.

Configurational force method enables fracture assessment in soft materials

Configurational mechanics offers a framework for quantifying the tendency of defects to alter the material configuration. When applied to fracture mechanics, configurational forces can be used to quantify the propensity of cracks to propagate. An alternative, well-established approach involves analytical solutions for crack tip displacement fields. However, these solutions typically apply to a limited range of constitutive behaviors and oftentimes to the linear small strain regime. The ease of calculating configurational forces in a numerical Finite Element implementation, along with their applicability to soft fracture at large strains, motivates the study of their performance as a standalone fracture framework. In contrast to the majority of works that remain theoretical and numerical, our study includes a robust experimental approach to configurational forces at finite strains. We report tensile experiments on a soft elastomer with pre-cuts ante fracture initiation. In a first attempt to approach the J-integral via configurational forces, we explore the performance of the linear elastic fracture mechanics solutions on Pacman-shaped domains that reproduce the crack tip vicinity. Then, we implement the entire boundary value problem with three-dimensional simulations that replicate the empirical tensile deformation of the soft elastomer samples. Subsequently, the results are benchmarked against estimations of the J-integral obtained through a bespoke finite strain analytical crack tip solution. With the successful validation of the configurational force method at finite strains, we aim to establish a pipeline for the calculation of configurational forces in a standalone manner and circumventing the need for close-form analytical solutions.

A comparison between FEM predictions and DIC results of crack tip displacement field in CT specimens made of titanium

In the context of fatigue crack growth (FCG), the validation of FEM predictions with experimental results has been made in terms of crack closure and da/dN. The objective here is to compare the prediction of the displacement field, which is the primary output of FEM, with experimental results obtained with Digital Image Correlation (DIC). The qualitative comparison indicates that DIC and FEM results are very similar. The comparison of CTOD curves obtained behind the crack tip showed a good agreement between the DIC and numerical predictions obtained under plane strain conditions. This indicates the dominance of the interior regions over the surface displacements, although the small thickness of the specimen (1 mm). The more detailed analysis of the CTOD loops, through the values of plastic CTOD ranges, showed a significant difference between FEM predictions and DIC results. The robustness of the numerical model was checked considering a mesh sensibility analysis, as well as considering different sets of material parameters in the simulation.

Modified Model of Crack Tip Stress Field Considering Dislocation Slip Accumulation and Crack Tip Blunting

This study uses the digital image correlation technique to measure the crack tip displacement field at various crack lengths in U71MnG rail steel, and the interpolated continuous displacement field was obtained by fitting with a back propagation (BP) neural network. The slip and stacking of dislocations affect crack initiation and growth, leading to changes in the crack tip field and the fatigue characteristics of crack growth. The Christopher-James-Patterson (CJP) model describes the elastic stress field around a growing fatigue crack that experiences plasticity-induced shielding. In the present work, this model is modified by including the effect of the dislocation field on the plastic zone of the crack tip and hence on the elastic field by introducing a plastic flow factor ρ, which represents the amount of blunting of the crack tip. The Levenberg-Marquardt (L-M) nonlinear least squares method was used to solve for the stress intensity factors. To verify the accuracy of this modified CJP model, the theoretical and experimental plastic zone errors before and after modification were compared, and the variation trends of the stress intensity factors and the plastic flow factor ρ were analysed. The results show that the CJP model, with the introduction of ρ, exhibits a good blunting trend. In the low plasticity state, the modified model can accurately describe the experimental plastic zone, and the modified stress intensity factors are more accurate, which proves the effectiveness of dislocation correction. This plastic flow correction provides a more accurate crack tip field model and improves the CJP crack growth relationship.

On the experimental characterisation of crack tip displacement fields on nonplanar elements: Numerical and experimental analysis

In this work, a numerical and experimental study about crack tip fields characterisation on curve-cracked elements has been performed. This study combines a novel differential geometry approach combined with 3D-DIC and FEA results to determine crack-tip parameters from the displacement field on a curved cracked element. The work aims to validate and compare some aspects that cannot be addressed using 3D-DIC. SIFs for different crack lengths are determined using DIC and FEA data and compared In addition, a comprehensive comparison between experimental and numerical fields is done using an Image Decomposition technique based on Tchebichef polynomials.

Towards a new methodology for the characterisation of crack tip fields based on a hybrid computational approach

This work presents a hybrid optimisation technique for the simultaneous calculation of crack tip characterising parameters and its spatial location, which can significantly affect the characterising parameters if the position used is inaccurate. The hybrid technique combines initial use of a genetic algorithm to obtain a well-conditioned set of initial parameter values that is then passed to an interior point optimisation algorithm for subsequent fast optimisation. Use of the hybrid technique is also amenable to easy automation. The capability of the technique is demonstrated using the CJP crack tip field model, with digital image correlation (DIC) being used to measure the 2D crack tip displacement field. This model was chosen, not only for its demonstrated sensitivity to accuracy in crack tip location, but also for its proven utility in providing effective crack growth correlation in the presence of plasticity-induced shielding across a wide range of growth rates. The results obtained from the hybrid technique are shown to be reliable through comparison with results obtained using other established techniques.

Characterization of non‐planar crack tip displacement fields using a differential geometry approach in combination with 3D digital image correlation

AbstractThis paper describes a novel differential geometry method that is used in combination with 3D digital image correlation (3D‐DIC) for crack tip field characterization on non‐planar (curved) surfaces. The proposed approach allows any of the two‐dimensional crack tip field models currently available in the literature to be extended to the analysis of a 3D developable surface with zero Gaussian curvature. The method was validated by analyzing the crack tip displacement fields on hollow thin‐walled cylindrical specimens, manufactured from either 304L or 2024‐T3 alloy that contained a central circumferential crack. The proposed approach was checked via a comparison between experimentally measured displacement fields (3D‐DIC) and those reconstructed from a modified 2D crack tip model (utilizing either 2, 3, or 4 terms of the William's expansion series) and implementing a 3D geometrical correction. Further validation was provided by comparing model‐derived stress intensity factors with values provided by empirical correlations.

Experimental evaluation of plastic wake on growing fatigue cracks from the analysis of residual displacement fields

AbstractA growing fatigue crack gives rise to a plastically deformed wake of material that envelops the crack. In this work, the plastic wake extent during fatigue crack growth is experimentally quantified by analyzing the crack tip displacement fields measured with digital image correlation. A novel technique based on use of a yield criterion is proposed that uses the undamaged state of the specimen as the reference state in the image processing. The plastic wake was identified by differentiation of the residual displacement fields obtained with a near‐zero load level to avoid any rigid body motion. The plastic wake extent was then found by assuming that the boundary between the elastic and plastic regions would occur when the equivalent stress was higher than the yield stress of the material. The results presented can contribute to a better understanding of the mechanisms driving fatigue crack propagation.

The mode I fatigue fracture of fine-grained quartz-diorite under coupled static loading and dynamic disturbance

In order to reveal the dynamic disturbance effect on the Mode I fatigue fracture behavior of hard rock, a series of three-point bending and disturbance fracture tests were performed on diorite specimens. Based on the plastic deformation ratio, a nonlinear degree p was proposed to correct the fracture toughness in disturbance fracture tests. The value of nonlinearity degree p increased with increasing pre-static load levels. As the disturbance frequency increases from 10 Hz to 40 Hz, the corrected fracture toughness with a pre-static load at 50%, 60%, 70%, and 80% of the peak load decreases by 17.04%, 13.63%, 12.17%, and 8.39%, respectively. When the pre-static load level increased from 50% to 70%, the number of cyclic loading-unloading increases, and then decreases as the pre-static level is more than 70%. Based on three-dimensional digital image correlation (3D-DIC) method, the displacement field near the notch tip is extracted and substituted into the crack tip displacement field equation to verify the accuracy of corrected fracture toughness. Finally, the size of fully developed fracture process zone (FPZ) is determined by extracting horizontal displacement (u)-horizontal distance (X) curves of reference lines from DIC system.

Fracture of 28 buckled two-dimensional hexagonal sheets

Mode-I stress intensity factors are estimated for 28 buckled two-dimensional hexagonal materials, including 6 mono-elemental (silicene, indiene, blue phosphorene, arsenene, antimonene and bismuthene) and 22 binary (CS, CSe, CTe, SiO, SiS, SiSe, SiTe, SiGe, GeO, GeS, GeSe, GeTe, SnO, SnS, SnSe, SnTe, SnGe, SnSi, InAs, InSb, GaAs and AlSb) two-dimensional materials. The crack-tip displacement field revealed from linear elastic fracture mechanics is adopted to find the stress intensity factor. Atomic-scale finite element method with Stillinger-Weber potentials is used to simulate the tensile tests. Mode-I stress intensity factors of these 28 two-dimensional materials appear ≤ 0.8 which are very small in comparison with boronitrene and graphene. Most of them exhibit their fracture toughness below 0.5 Our findings are helpful in the design of nano-devices with these two-dimensional materials.

Numerical Analysis of Mode I Fracture Toughness for Plain Concrete Beams

Fracture mechanics is based on the assumption that all engineering materials contain cracks from which failure starts. Structures have sizeable existing cracks that might or might not grow, depending on the load level. when a material has an existing crack, that lead to high stresses near the crack tip. Stress field type in the region of the crack tip can be defined of mode I, where two fracture surfaces are displaced perpendicular to each other in opposite direction where crack growth takes place. The crack tip stress and displacement field can be uniquely characterized by the stress intensity factor, SIF, It is neither the magnitude of stress nor strain, but it is a unique parameter that describes the effect of loading at the crack tip region and the resistance of the material. Stress intensity filed is valid for a small region around the crack tip. It depends on both the values of stress and crack size. In the present work, numerical models were designed to study the effect of specimen thickness, crack-depth ratios and concrete compressive strengths on the behavior of SIF for concrete beams. Nine beams were idealized with dimensions of 1500 mm length, 400 mm depth and different thickness 120, 250 and 400 mm. The crack-depth ratios were 0.1, 0.2 and 0.3 and the concrete compressive strengths were 25, 40 and 55 MPa. The results proved that there is a decrease in SIF with increase in specimen thickness. On the other hand; there is an increase in SIF values with increase in concrete compressive strength and crack-depth ratio.

Evaluation of the SIF and T-stress values of the Brazilian disc with a central notch by hybrid method

The near-crack-tip displacement field of a Brazilian disc with a central notch (BDCN) under mixed mode I/II conditions was measured via digital image correlation (DIC) and the stress intensity factor (SIF) was estimated using a hybrid method that allowed the fitting of the experimental data into the Williams series expansion. The effects of higher-order terms in the Williams expansion (T-stress) were analysed for different sizes of the crack tip fitting region and the results were compared with analytical predictions as well as with results obtained based on the numerically calculated crack-tip displacement field.

Experimental characterisation of fatigue crack growth based on the CTOD measured from crack tip displacement fields using DIC

The current work presents an experimental study on the use of the crack tip opening displacement (CTOD) to evaluate its ability to characterise fatigue crack growth. A methodology is developed to measure and to analyse the CTOD from experimental data. The vertical displacements obtained by implementing digital image correlation (DIC) on growing fatigue cracks are used to measure the CTOD. Two fatigue tests at stress ratios of 0.1 and 0.6 were conducted on compact tension (CT) specimens manufactured from a 1 mm thick sheet of commercially pure titanium. A sensitivity analysis to explore the effect of the position selected behind the crack tip for the CTOD measurement was performed. The analysis of a full loading cycle allowed identifying the elastic and plastic components of the CTOD. The plastic CTOD was found to be directly related to the nonlinear zone (i.e., plastic deformation) generated at the crack tip during fatigue propagation. Moreover, a linear relationship between da/dN and ΔCTODp independent of the stress ratio was found. Results show that the CTOD can be used as a viable alternative to the stress intensity factor range (ΔK) in characterising fatigue crack propagation since the parameter considers the fatigue threshold and crack shielding in an intrinsic way.

Investigation of effective stress intensity factors during overload fatigue cycles using photoelastic and DIC techniques

This work uses DIC and photoelastic techniques to investigate the effect of single overload cycles applied during constant amplitude fatigue. Effective values of the range of stress intensity factor were calculated using the CJP model of crack tip stress and displacement fields, as this model considers both wake contact and compatibility-induced influences on the applied elastic field arising from the plastic enclave generated around a fatigue crack. Values of the effective stress intensity factor are related to the observed crack growth acceleration and retardation. In addition, the paper compares the CJP results with those obtained using a compliance-based method. The present work demonstrates the utility of the CJP model in characterising fatigue crack growth rates during variable amplitude loading. It is also possible with the CJP model, through changes in the coefficient values and hence, for the first time, to shed explicit light on the contributions made by different mechanisms to the shielding effects of an overload.

Fracture analysis in plane structures with the two-scale G/XFEM method

Generalized or extended finite element method (G/XFEM) uses enrichment functions that holds a priori knowledge about the problem solution. These enrichment functions are mostly limited to two-dimensional problems. A well-established solution for problems without any specific types of analytically derived enrichment functions is to use numerically-build functions in which they are called global-local enrichment functions. These functions are extracted from the solution of boundary value problems defined around the region of interest discretized by a fine mesh. Such solution is used to enrich the global solution space through the partition of unity framework of the G/XFEM. Here it is presented a two-scale/global-local G/XFEM approach to model crack propagation in plane stress/strain and Reissner–Mindlin plate problems. Discontinuous functions along with the asymptotic crack-tip displacement fields are used to represent the crack without explicitly represent its geometries. Under the linear elastic fracture mechanics approach, the stress intensity factor (obtained from a domain-based interaction energy integral) can be used to either determine the crack propagation direction or propagation status, i.e., the crack can start to propagate or not. The proposed approach is presented in detail and validated by solving several linear elastic fracture mechanics problems for both plane stress/strain and Reissner–Mindlin plate cases to demonstrate its the robustness and accuracy.

Mode-I stress intensity factors of silicene, AlN, and SiC hexagonal sheets

The crack-tip displacement field and molecular dynamics finite element method with Tersoff potentials were used to find the mode-I stress intensity factors (SIF) of silicene, aluminum nitride (AlN), and silicon carbide (SiC) hexagonal sheets. Fracture properties of graphene and boronitrene are also included for comparison. It is found that KIct (KIc is mode-I critical SIF and t is the sheet’s thickness) of silicene, AlN, and SiC sheets are approximately 80, 66, and 47%; and 73, 64, and 45% smaller values of those of graphene for crack along the armchair and zigzag directions, respectively. The estimated fracture toughness of silicene is close to the experimental data of single-crystal silicon.

New insight on physical meaning of fracture criteria for growing cracks

Because plastic unloading is inevitable during crack growth in elastic plastic materials, the J integral is not applicable anymore, and several path-independent integrals are thus proposed by different authors to overcome this limitation. In this paper, we start from the crack tip energy flux. We first derive two important formulas and then find that these path-independent integrals are in fact identical to each other and consistent with the crack tip energy flux. That is, the crack tip energy flux is more essential for growing cracks in elastic plastic materials. In addition, a force such as crack tip parameter, which is conjugated to crack tip velocity, is proposed by us on the perspective that crack tip energy flux can be considered as the power dissipated by crack tip due to crack growth. This parameter is proved to be the absolute value of the projection of the crack tip configurational force vector into the direction of the nominal crack growth direction, and thus, this parameter is the thermodynamic crack driving force. Moreover, this parameter can represent crack tip stress and displacement fields of growing cracks, and thus, a fracture criterion based on this parameter is proposed. The critical value of this parameter corresponds to the rate of energy dissipated in the fracture process zone per unit crack extension.

A more effective rationalisation of fatigue crack growth rate data for various specimen geometries and stress ratios using the CJP model

This paper demonstrates that the CJP model of crack tip stresses, through its ability to directly predict the effective range of stress intensity factor, also provides an improved rationalisation of fatigue crack growth rate across several different specimen geometries and stress ratios. This aim is achieved through a comparison between the crack growth rate rationalisation obtained using the CJP stress intensity factor range, ΔKCJP, and that derived from the standard Irwin definition of ΔK = Kmax − Kmin. The results demonstrate a significant improvement arising from the use of the CJP stress intensity factors and also highlight the fact that the CJP crack tip field model does not require the incorporation of compliance-based geometry-correction factors in the calculation of stress intensity. Fatigue crack growth rate tests were carried out on compact tension (CT) and double edge-notched tension (DENT) specimens of Grade 2 titanium at various stress ratios between 0.05 and 0.6 whilst making simultaneous crack tip displacement field measurements using the digital image correlation (DIC) technique. The DIC data were then processed to obtain the CJP stress intensity factors KF and KR. Calculation of the CJP stress intensity factors is relatively complex and rests on the acquisition of displacement field data. In order to facilitate simplified prediction of crack growth rates using the CJP model, this paper also determines a relationship between ΔKCJP and ΔK using calibration curves that relate the values of the parameters in the CJP model to the standard ΔK value.

Crack tip displacement fields measured by digital image correlation for evaluating variable mode-mixity during fatigue crack growth

The assessment of mixed-mode fatigue is an actual object of research. Various hypotheses have been published with the focus on calculating equivalent stress intensity factors and on predicting kink angles after a change of mode-mixity from one cycle to the next. Relatively few works are known for cases when the mode-mixity changes continuously during the fatigue cycles. Such investigations on determining equivalent stress intensity factors and their effects on crack growth have been performed in the present study. Thin-walled tubes with a through-wall crack have been loaded by proportional and non-proportional tension and torsion.In the experimental investigation, the region of fatigue crack growth was observed by means of applying the digital image correlation technique. The variations of the displacement fields during the cycles are shown. Depending on the ratio of applied loads as well as on the actual orientation of the crack tip tangent, fracture parameters associated with opening modes I, II and III are identified, not only during a cycle but also from cycle to cycle.As the crack path is known from experiment, its curvature – both kinks and continuously developing warped cracks were observed – may be attributed to the variation of the displacement field. Results of ongoing work are presented in this paper.Modelling crack closure is a special challenge. Closure is clearly visible in the measurement. It is a combination of conventional plasticity induced closure and roughness induced closure; on top, the curvature of the cracks enforces a geometrical type of crack flank locking.

Two-dimensional fracture modeling with the generalized/extended finite element method: An object-oriented programming approach

This work presents an object-oriented implementation of the G/XFEM to model the crack nucleation and propagation in structures made of either linear or nonlinear materials. A discontinuous function along with the asymptotic crack-tip displacement fields are used to represent the crack without explicitly meshing its surfaces. Different approach are explained in detail that are used to capture the crack nucleation within the model and also determine the crack propagation path for various problems. Stress intensity factor and singularity of the localization tensor (which provides the classical strain localization condition) can be used to determine the crack propagation direction for linear elastic materials and nonlinear material models, respectively. For nonlinear material model, the cohesive forces acting on the crack plane are simulated in the enrichment process by incorporating a discrete constitutive model. Several algorithms and strategies have been implemented, within an object-oriented framework in Java, called INSANE. This implementation will be presented in detail by solving different two-dimensional problems, for both linear and nonlinear material models, in order to show the robustness and accuracy of the proposed method. The numerical results are compared with the reference solutions from the analytical, numerical or experimental results, where applicable.