Measurement of Fracture Parameters for a Mixed-Mode Crack Driven by Stress Waves using Image Correlation Technique and High-Speed Digital Photography

Abstract:  Measurement of fracture parameters for a rapidly growing crack in syntactic foam sheets using image correlation technique and high-speed photography is presented. The performance of a rotating mirror-type multi-channel high-speed digital camera to measure transient deformations is assessed by conducting benchmark tests on image intensity variability, rigid translation and rigid rotation. Edge-cracked foam samples are subjected to eccentric impact loading relative to the initial crack plane to produce mixed-mode loading conditions in a three-point bend configuration. High-speed photography is used to record decorated random speckles in the vicinity of the crack tip at a rate of 200 000 frames per second. Two sets of images are recorded, the first set before impact and the second after impact. Using image correlation methodology, crack-tip displacement field histories and dominant strains from the time of impact up to complete fracture are mapped. Over-deterministic least-squares analyses of crack-tip radial and tangential displacements are used to obtain mixed-mode fracture parameters. The measurements are compared with complementary finite element results. The fracture parameters determined from radial displacements seem more robust even when fewer number of higher order terms in the crack-tip asymptotic expansion are used.     

Investigation of fatigue crack closure using multiscale image correlation experiments

Two full-field macroscale methods are introduced for estimating fatigue crack opening levels based on digital image correlation (DIC) displacement measurements near the crack tip. Crack opening levels from these two full-field methods are compared to results from a third (microscale) method that directly measures opening of the crack flanks immediately behind the crack tip using two-point DIC displacement gages. Of the two full-field methods, the first one measures effective stress intensity factors through the displacement field (over a wide region behind and ahead of the crack tip). This method reveals crack opening levels comparable to the limiting values (crack opening levels far from the crack tip) from the third method (microscale). The second full-field method involves a compliance offset measurement based on displacements obtained near the crack tip. This method delivers results comparable to crack tip opening levels from the microscale two-point method. The results of these experiments point to a normalized crack tip opening level of 0.35 for R ∼ 0 loading in grade 2 titanium. This opening level was found at low and intermediate ΔK levels. It is shown that the second full-field macroscale method indicates crack opening levels comparable to surface crack tip opening levels (corresponding to unzipping of the entire crack). This indicates that effective stress intensity factors determined from full-field displacements could be used to predict crack opening levels.     

Quantifying crack tip displacement fields with DIC

Crack paths under both fatigue and fracture conditions are governed by the crack tip displacement field and the material deformation characteristics, including those influenced by metallurgical anisotropy. Experimental techniques such as thermoelasticity and photoelasticity have been successfully used to characterise the elastic stress fields around cracks but they do not take into account either plasticity or anisotropy. Considerable work has been carried out to characterise crack tip stress fields from displacement measurements. The current method of choice for obtaining displacement field data is digital image correlation (DIC) which has undergone significant advances in the recent years. The ease of use and capabilities of the technique for full field displacements has led to improved methods for characterising crack tip displacement fields based on data obtained from DIC. This paper gives an overview of some of the applications of DIC for crack tip characterisation such as K, T-stress and crack tip opening angle (CTOA) measurements as well as data obtained from 3D measurements of a propagating crack.     

Fatigue crack growth in Haynes 230 single crystals: an analysis with digital image correlation

Fatigue crack growth was investigated in Haynes 230, a nickel‐based superalloy. Anisotropic stress intensity factors were calculated with a least squares algorithm using the displacements obtained from digital image correlation. Crack opening/sliding levels were measured by analysing the relative displacement of crack flanks. Reversed crack tip plastic zones were calculated adopting an anisotropic yield criterion. The strains measured in the reversed plastic zone by digital image correlation showed a dependence on crystallographic orientation. Finally, a finite element model was adopted to examine plasticity around the crack tip. Results were compared with the experimentally observed strains.     

Smoothing Measured Displacements and Computing Strains Utilising Finite Element Method

Abstract: A method for smoothing measured displacements and computing strains utilising finite element and least‐squares methods is proposed. Nodal displacement values of a finite element model are determined by fitting the interpolation functions of elements to measured displacement values using the method of least‐squares. The displacements in the region where the measurement values are not obtained or unreliable are determined by solving finite element equations. Then, strains are obtained using a displacement‐strain relationship. The validity is demonstrated by applying the proposed method to the displacement distributions of a plate with a hole obtained using finite element method and those around a crack tip obtained using digital image correlation. Results show that the displacements and the strains can be determined accurately by the proposed method. Furthermore, the strains near free boundaries and strain concentration region can be computed. As strains can be evaluated easily and accurately, the proposed method can be used as one of the data processing methods for optical methods.     

Determination of displacements around fatigue cracks using image analysis of in‐situ scanning electron microscope images

A technique to in‐situ measure the displacements in the vicinity of the crack tip during fatigue crack propagation has been developed. High‐resolution images of the crack tip were taken continuously throughout the fatigue load cycles with a scanning electron microscope (SEM), and an image analysis program was used to determine the displacements at different positions with respect to the crack tip. The displacements were then used to determine crack shapes and compliance curves. The measured crack shapes show a general √r dependence versus the distance to the crack tip. However, close to the crack tip the crack shape is clearly affected by plastic deformation, even in cases when small scale yielding prevails. The compliance curve measurements close to the crack tip can be used to determine the global stress level when the crack surfaces are separated, so that the exact opening and closure stresses can be determined.     

A combined experimental-numerical investigation of crack growth in a carbon–carbon composite

A combined experimental–numerical investigation of crack growth in a carbon–carbon composite is reported. In this material, both matrix fracture and fibre bridging contribute significantly to toughness. Crack growth experiments were performed using side‐notched DCB specimens with doublers. A digital image correlation method was used to measure displacements fields on the specimen surfaces, crack extension and crack opening profiles. An effective cohesive zone law was determined from the experimental data. The effective cohesive zone law is subsequently separated into the individual contributions from matrix cracking and fibre bridging. Numerical simulation of crack growth based on this cohesive zone law and experimental data are in good agreement. Special focus of the numerical study is on the investigation of the discontinuous nature of crack growth.     

Digital image correlation measurement of near‐tip fatigue crack displacement fields: constant amplitude loading and load history effects

Recent work by de Matos and colleagues employed digital image correlation to measure near tip displacement fields for fatigue cracks in 6082 T6 aluminium alloy. The main focus of this work was to directly measure fatigue crack closure, but the measurements can also be used to examine conditions at and ahead of the crack tip. In this paper, the results are re‐analysed and compared to two crack‐tip deformation models. The first assumes simple elastic deformation (according the Westergaard solution). This allows the history of crack‐tip stress intensity to be examined. Reasonable agreement with the elastic model is obtained, although there is a residual stress intensity caused by the plastic wake, which gives rise to crack closure. The second model examined is a simple elastic–plastic assumption, proposed by Pommier and colleagues. This can be applied to constant amplitude loading, although the results obtained here are very similar to the elastic case. A slightly more complex load case (a single overload in an otherwise constant amplitude variation of load) gives a much more complicated crack‐tip history. Here, the importance of crack‐tip plastic displacement, represented by the second term in Pommier's model becomes much clearer. Load history effects are captured by the residual value of this term and its associated displacement fields as well as by stress intensity factor. The implications for further modelling and experimental work are discussed.     

Crack resistance behavior of particulate reinforced composites at various test speeds and temperatures

In this study, the fracture behavior and characteristics of particulate-reinforced composite materials were evaluated by performing wedge splitting tests. The crack resistance of the materials was evaluated using the crack tip opening displacement and crack tip opening angle. The composites were tested under various temperatures and test speeds. The digital image correlation method was used to analyze the strain field at the crack tip. The fracture surface under test conditions was observed using a scanning electron microscope. The test results showed that the fracture energy increased with decreasing temperature, and the crack resistance increased with increasing test speed. The crack tip opening angle is divided into an unstable region and stable region. The critical crack tip opening angle can be defined as the fracture mechanics parameter measured in a stable region. The surface strain fields obtained by digital image correlation method are distributed in the range from 1.5 % to 4.5 % at the initiation of the crack. A crack grows with dewetting phenomenon at the temperature range from 60 °C to −40 °C, and the crack propagates with fracture of ammonium perchlorate oxidizer particles at the glass transition temperature of −70 °C.     

Quasi-static and dynamic fracture of graphite/epoxy composites: An optical study of loading-rate effects

Strain-rate effects on fracture behavior of unidirectional composite materials are studied. Single-edge notched multi-layered unidirectional graphite composites (T800/3900-2) are investigated to examine fracture responses under static and dynamic loading conditions using a digital speckle correlation method. The fracture parameters for growing cracks are extracted as a function of fiber orientation. A 2D digital image correlation (DIC) method is used to obtain time-resolved full-field in-plane surface displacements when specimens are subjected to quasi-static and impact loading. Stress intensity factor and crack extension histories for pure mode-I and mixed mode cases are extracted from the full-field displacements. When compared to the dynamic stress intensity factors at crack initiation, the static values are found to be consistently lower. The stress intensity factor histories exhibit a monotonic reduction under dynamic loading conditions whereas an increasing trend is seen after crack initiation under quasi-static loading cases. This is potentially due to dominant crack face fiber bridging effects in the latter cases.     

Stress intensity factors and CODs defined by in-plane displacements measured by scanning electron microscopy

A method is developed for evaluating the displacement field around the tip of a crack in a plate under plane stress or strain conditions by executing a number of measurements in this area through the scanning electron microscope. Several spots were created around the crack tip by using the electron beam of the SEM, which were used as reference points. A theory was developed which yields the components of the in-plane displacements and their differences from the coordinates of the reference spots measured through SEM. The method presents the advantage that its results are independent of the exact position of the crack tip and therefore it is suitable for performing measurements very close to this tip. Experimental evidence with plexiglas plates showed the validity of the method for defining the displacement field as well as the values of crack opening displacements and the stress intensity factor.     

Fatigue crack closure: A myth or a misconception?

In this paper, we have extended our previous study on fatigue crack closure to examine the phenomenon of crack opening displacement (COD) and its impact on the crack tip fields in both 2D and 3D specimen geometries using full‐field experimental measurements and integrated finite element modelling. Digital image correlation (DIC) and digital volume correlation (DVC) were used to measure the near‐tip material responses on the surfaces (DIC) and the interior (DVC) of the specimens. Materials with elastic‐plastic and large plastic characteristics were chosen for the study, where plasticity‐induced premature contact between the crack flanks is known to occur. Displacement maps around the cracks were obtained using DIC and DVC at selected load increments and were introduced as boundary conditions into the finite element (FE) models to obtain the “effective” crack driving force in terms of J‐integral, and the results were compared with those “nominal” from the standard FE analysis. Both visual observation and compliance curves were used to determine the “crack opening” levels; whilst the impacts of the crack opening on the crack driving force J and the normal strains ahead of the crack tip were evaluated in 2D and 3D. The results from the study indicate that, crack closure, although clearly identifiable in the compliance curves, does not appear to impact on global crack driving force, such as J‐integral, or strains ahead of the crack tip; hence, it may well be a misconception.     

Full‐field characterisation of crack tip deformation and fatigue crack growth using digital image correlation—a review

In recent years, digital image correlation has been widely used in the analysis of crack problems. This review will examine digital image correlation, as a full‐field measurement technique, in the studies of crack tip mechanical behaviour under cyclic loading conditions. In particular, topics including determination of fracture mechanics parameters and evaluation of crack closure will be discussed. Micromechanical aspects of crack growth under cyclic loading will also be explored in crack driving and attenuation effects.     

Determination of Stress Intensity Factor for Cracks in Orthotropic Composite Materials using Digital Image Correlation

Abstract: This paper focuses on the application of the digital image correlation (DIC) technique to determine the stress intensity factor (SIF) for cracks in orthotropic composites. DIC is a full‐field technique for measuring the surface displacements of a deforming object and can be applied to any type of material. To determine the SIF from full‐field displacement data, the asymptotic expansion of the crack‐tip displacement field is required. In this paper the expansion of the crack tip displacement field is derived from an existing solution for strain fields. Unidirectional fibre composite panels with an edge crack aligned along the fibre were tested under remote tensile loading and the displacements were recorded using DIC. The SIF was calculated from the experimental data by fitting the theoretical displacement field using the least squares method. The SIF thus determined was in good agreement with theoretical results and therefore demonstrates the applicability of the derived displacement field and DIC technique for studying fracture in composites.     

The effect of shallow cracks on crack tip opening displacement

Further results given in the present paper confirm that shallow cracks have larger crack tip opening displacements at initiation than deep cracks. This difference in behaviour is shown to be principally caused by the different hydrostatic stresses existing at the tips of shallow and deep cracks. A new method based on lateral crack growth across the thickness is used in this work to measure crack tip opening displacements in specimens containing machined slots rather than fatigue pre-cracks. Justification and advantages of this method are discussed and compared to the conventional technique.     

An analytical method for mixed-mode propagation of pressurized fractures in remotely compressed rocks

An analytical method for mixed-mode (mode I and mode II) propagation of pressurized fractures in remotely compressed rocks is presented in this paper. Stress intensity factors for such fractured rocks subjected to two-dimensional stress system are formulated approximately. A sequential crack tip propagation algorithm is developed in conjunction with the maximum tensile stress criterion for crack extension. For updating stress intensity factors during crack tip propagation, a dynamic fictitious fracture plane is used. Based on the displacement correlation technique, which is usually used in boundary element/finite element analyses, for computing stress intensity factors in terms of nodal displacements, further simplification in the estimation of crack opening and sliding displacements is suggested. The proposed method is verified comparing results (stress intensity factors, propagation paths and crack opening and sliding displacements) with that obtained from a boundary element based program and available in literatures. Results are found in good agreements for all the verification examples, while the proposed method requires a trivial computing time.     

Analysis of the Elastoplastic Deformation of the Material in the Process Zone

By the method of digital correlation of speckle images, we record the displacements in the vicinity of the crack tip in plane specimens of D16AT alloy. The field of elastoplastic displacements is determined in the vicinity of the crack tip under static loading. By using the distribution of displacements, we compute the levels of strains ε _y on the continuation of the crack. The theoretical results are in good agreement with the experimental data in estimating the length of the plastic zone for the limiting equilibrium state.__________Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 40, No. 5, pp. 67–72, September–October, 2004.     

Plastic CTOD as fatigue crack growth characterising parameter in 2024‐T3 and 7050‐T6 aluminium alloys using DIC

The plastic range of crack tip opening displacement (CTOD) has been used for the experimental characterisation of fatigue crack growth for 2024‐T3 and 7050‐T6 aluminium alloys using digital image correlation (DIC). Analysis of a complete loading cycle allowed resolving the CTOD into elastic and plastic components. Fatigue tests were conducted on compact tension specimens with a thickness of 1 mm and a width of 20 mm at stress ratios of 0.1, 0.3 and 0.5. The range of plastic CTOD could be related linearly to da/dN independent of stress ratio for both alloys. To facilitate accurate measurements of CTOD, a method was developed for correctly locating the crack tip and a sensitivity analysis was performed to explore the effect of measurement position behind the crack tip on the CTOD. The plastic range of CTOD was demonstrated to be a suitable alternate parameter to the stress intensity factor range for characterising fatigue crack propagation. A particularly innovative aspect of the work is that the paper describes a DIC‐based technique that the authors believe gives a reliable way to determine the appropriate position to measure CTOD.     

Plastic zone size estimation under cyclic loadings using in situ optical microscopy fatigue testing

An in situ optical microscopy fatigue testing is proposed in this paper to investigate the forward and reversed plastic zone size under cyclic loadings for Al‐7075‐T6. This experimental study is used to verify the hypotheses in a recently developed small time scale formulation of fatigue crack growth. During the testing, the entire cyclic loading cycle is divided into a certain number of steps. Images of the crack tip are taken at each step. The full strain field around the crack tip is determined using the digital image correlation (DIC) technique. The plastic zone size is obtained by combining the DIC results and the material constitutive relationship. Experimental measurements from the proposed study are compared with theoretical predictions. It is observed that the crack closure has a large effect on the reversed plastic zone size. The plastic zone size remains almost constant when the unloading path is below a certain stress level, which is one of the hypotheses used in a previous crack growth model. Discussions are given for the modelling of plastic zone size variation under cyclic loadings and several conclusions are drawn based on the current investigation.     

Analytical calculation of stress intensity factor of cracked steel I-beams with experimental analysis and 3D digital image correlation measurements

An analytical method to calculate the stress intensity factor for cracked steel I-beams under both bending moment and axial load is presented. The method is based on the approach of crack surface widening energy release rate. The crack surface widening energy release rate is formulated by a G^∗-integral and elementary strength theory of materials. Comparisons between the analytical results and results available in the literature for specific cases demonstrate the validity of the methodology. Furthermore, the fatigue and fracture behavior of the steel I-beam are experimentally investigated. The fatigue crack growth rate, residual deflection and stiffness reduction of a cracked beam under cyclic loading are studied. A three-dimensional digital image correlation system is used to illustrate the stress evolution pattern and the plasticity zone around the crack tip using image processing technique, thereby providing further verification of the theoretical models.