Double Cleavage Drilled Compression Research Articles

Simulating the onset of damage in DCDC tests using a novel gradient‐extended damage model for tension‐compression asymmetry

AbstractIn the present work, an existing framework for gradient‐extended damage is extended to simulate the damage onset in double cleavage drilled compression (DCDC) tests. The main idea is to consider the different evolution of the damage variable under tensile and compressive loading. More specifically, the star‐convex decomposition is exploited to split the strain energy into an active part and an inactive part, and only the active part drives the evolution of the damage variable in the compressive regime. A parameter adopted in the star‐convex decomposition is applied to calibrate the compressive strength independently from the tensile strength, such that the current model can simulate different types of the damage onset. Furthermore, the strengthening effect induced by damage hardening is discussed in this work.

3D analysis of crack propagation in nuclear graphite using DVC coupled with finite element analysis

The initiation and propagation of cracks within nuclear graphite components compromise the lifespan of advanced gas-cooled reactors and even lead to safety incidents. A thorough understanding of fracture properties in nuclear graphite is crucial for the effective management and design of graphite structural components. In this work, an in-situ test of a double cleavage drilled compression (DCDC) specimen was conducted using X-ray tomographic imaging to fully analyze the 3D crack propagation behavior in IG-11 nuclear graphite. “Subvolume Splitting” digital volume correlation (SS-DVC) was employed to accurately quantify the displacement fields surrounding the crack. The entire 3D crack propagation and crack surface around the crack front were precisely captured through 3D imaging processing of the gray level residual (GLR) field. Additionally, crack opening displacements (CODs) and stress intensity factors (SIFs) were determined using finite element (FE) analysis with extended finite element method (XFEM). Experimental results indicate that although mode I crack remains predominant throughout the whole process, complex crack propagation exists around the crack front. The utilization of irregular crack surfaces in FE analysis helps to obtain refined displacement fields and accurate SIFs of the crack front. This work provides comprehensive insights into crack propagation and reveals the influence of complex crack morphology on SIF calculations, facilitating accurate prediction of structural integrity and rational design of graphite components.

Comparison of Mode I fracture toughness of an elastic and an elastoplastic methyl methacrylate polymer as measured by SENB and DCDC tests

An elastic and an elastoplastic methyl methacrylate polymer, both in the glassy state, have been submitted to mode I fracture characterization with two different tests, the single edge notch bending (SENB) and the double cleavage drilled compression (DCDC) tests. The elastic material toughness was simply assessed by the linear elastic fracture mechanics analysis. For the elastoplastic material, the J-integral was computed when the strain fields were available. Moreover, numerical analyses were carried out using finite element simulations with a phase-field damage approach, providing comparison when the J-integral had been calculated and estimate otherwise, of the critical energy release rate. For each material, as well as for each test, the values of the critical energy release rate that have been estimated here, are in good agreement with the literature. More interestingly, for the same material, both tests provide with very different estimates of this material parameter, leaving engineers uncertain on which test to choose to assess the material toughness in crack opening mode.

Fracture toughness evaluation of a nuclear graphite with non-linear elastic properties by 3D imaging and inverse finite element analysis

Effective small specimen tests are needed to obtain fracture toughness and elastic properties as the limited availability of irradiated graphite restricts the quantity and dimensions of test specimens. Both properties have evaluated simultaneously in a crack propagation test with the double cleavage drilled compression (DCDC) specimen geometry of a fine-grained graphite (SNG742) that has non-linear elastic properties in the unirradiated condition. Three-dimensional displacement fields were obtained by digital volume correlation of in situ laboratory X-ray computed tomographs, and the 3D crack geometry (crack tip position, crack opening displacements and angle) was determined objectively by a wavelet variance method. The tensile softening of the Young modulus was determined by inverse analysis of the strain field using the finite element model updating (FEMU) method. The strain energy release rate of the quasi-static propagating crack was calculated using the contour integral method in a finite element model with the derived non-linear elastic properties and the measured displacements as boundary conditions. The critical strain energy release rate was constant with crack length (118 ± 14 J m−2) and equivalent to a fracture toughness of 1.13 ± 0.07 MPa m1/2.

Scrutinized and revised stress intensity factor formulas for double cleavage drilled compression specimens

First, we critically review the stress intensity factor formulas for double cleavage drilled compression (DCDC) specimens, and prove the highly acclaimed analytical formulas for the DCDC were erroneously formulated in Plaisted et al. (2006), we detail the reasons for the errors in several integrals with a short-crack model, and in expressions for bending moment and moment of inertia with a long-crack mode, extending the brief argument in Wang et al. (2016). Then, revised stress intensity factor formulas for DCDC derived by curve-fitting the results from finite element analysis are given, which are applicable to wide-ranging specimen geometries beyond that prescribed in He et al. (1995). Finally, it is shown that even with a load-controlled loading, crack growth stability for DCDC is guaranteed for the whole fracturing process in the experiment, excluding only the DCDC with very small crack length, this is a unique and useful feature pertaining to the DCDC for testing brittle materials.

Effect of shape memory alloy wires on the enhancement of fracture behavior of epoxy polymer

The effect of embedded shape memory alloy (SMA) wires on the fracture behavior of epoxy resin was studied. A micromechanical model was developed to predict the double cleavage drilled compression (DCDC) test results for SMA reinforced epoxy specimens. The DCDC tests were performed on SMA reinforced epoxy and the fracture behavior of specimens with different crack lengths was investigated. The experimental tests were conducted on the specimens with 1%, 2% and 4% pre-strain levels in order to investigate the enhancement of crack growth resistance (KR) in the epoxy polymer. The effects of SMA wire diameter, temperature change and applied pre-strain level on the fracture behavior of SMA reinforced epoxy were studied using the present model. The results showed a 67% increase in the changes in the crack growth resistance (KR) in 1% pre-strained SMA reinforced epoxy subjected to temperature change from 25 °C to 65 °C. This improvement was 38% and 16% for the 2% and 4% SMA pre-strained reinforced epoxy, respectively. The results also revealed that, at constant temperature (T = 65 °C), 2% and 4% pre-strains improved (KR) of epoxy by 2 and 4 times, respectively, in comparison with the case of 1% pre-strained wires. The effect of the interface region between SMA wires and epoxy was also discussed in the present study.

A multi-channel setup to study fractures in scintillators

To investigate fractoluminescence in scintillating crystals used for particle detection, we have developed a multi-channel setup built around samples of double-cleavage drilled compression (DCDC) geometry in a controllable atmosphere. The setup allows the continuous digitization over hours of various parameters, including the applied load, and the compressive strain of the sample, as well as the acoustic emission. Emitted visible light is recorded with nanosecond resolution, and crack propagation is monitored using infrared lighting and camera. An example of application to (BGO) is provided.

Clarification of formulas for stress intensity factor for DCDC specimens

A correction is provided to the formula for the stress intensity factor for the double cleavage drilled compression (DCDC) specimen derived by Plaisted et al. in Int J Fract 141: 447–457, 2006.

Interfacial fracture strength and toughness of copper/epoxy-resin interfaces

We present results examining the interfacial fracture toughness of Cu2O/epoxy-resin interfaces, which is an important parameter in microelectronic packaging design. Tensiometer measurements of the epoxy-resin surface energy together with contact angle measurements of epoxy-resin/Cu2O wetting yield an estimate of the thermodynamic work of adhesion of 0.074 Jm−2. Double cleavage drilled compression (DCDC) and pull test samples were used to evaluate the critical stress intensity and strain energy release rate for interface fracture and found to be 0.05 MPa-m1/2 and 1.4 Jm−2. These sample geometries yielded only interface failure with no trace of fracture occurring in either the copper or the epoxy-resin component. The difference between the values of the thermodynamic work of adhesion and the critical strain energy release rate is attributed to plastic processes most likely occurring in the copper layer of the sandwich sample configuration of the DCDC sample.

An empirical model for estimating fracture toughness using the DCDC geometry

The double cleavage drilled compression (DCDC) geometry is useful for creating large cracks in a material in a controlled manner. Several models for estimating fracture toughness from DCDC measurements have been proposed, but each is suitable for a subset of geometries and material properties. In this work, a series of finite element fracture simulations are performed over a range of sample widths, hole sizes, heights, Young’s moduli, Poisson’s ratios, critical stress intensity factors, and boundary conditions. Analyzing the simulation results, fracture toughness is found to be a simple function of sample width, hole size, and an extrapolated stress at zero crack length obtained from a linear fit of the data. Experimental results in the literature are found to agree with this simple relationship.

The effect of geometry on fracture strength measurement using DCDC samples

The fracture behavior of poly(methyl methacrylate) (PMMA) is studied using double cleavage drilled compression (DCDC) experiments. Increasing sample thickness is found to increase the stresses required to propagate long cracks. Crack surface features show a correlation with regimes of crack growth. Decreasing hole size leads to significant inelastic deformation during testing and, after unloading, the formation of new stress-relieving cracks at the central hole. A computational model using the experimental data estimates the critical stress intensity factor of PMMA to be 0.6–0.75MPam½. Photoelastic observations are used to compare experimentally observed and simulated stress distributions.

Numerical analysis of an improved DCDC specimen for investigating mixed mode fracture in ceramic materials

Double cleavage drilled compression (DCDC) specimen, on account of its specific fracture parameters and also strong crack path stability, is frequently used in crack growth studies of brittle materials such as ceramics and glasses. Various configurations of this specimen have been developed and studied in the past in order to determine fracture parameters in different loading conditions. In this paper, an improved DCDC specimen is proposed by means of some geometrical modifications applied to the standard DCDC configuration. Finite element analyses indicate that contrary to all previous DCDC configurations, the new version has the distinct potential to provide the entire span of practical loading condition from pure mode I to pure mode II. It is also shown that the T-stress term is strongly negative in this specimen. Using a generalized maximum tangential stress (MTS) criterion, the T-stress effects on fracture initiation of the proposed specimen are investigated analytically.

Crack opening profile in DCDC specimen

The opening profile of the cracks produced in the Double Cleavage Drilled Compression (DCDC) specimens for brittle materials is investigated. The study is achieved by combining Finite element simulations of a DCDC linear elastic medium with experimental measurements by crack opening interferometry on pure silica glass samples. We show that the shape of the crack can be described by a simple expression as a function of the geometrical parameters of the sample and the external loading conditions. This result can be used to measure accurately in real time relevant quantities during DCDC experiments, such as the crack length or the stress intensity factor applied to the specimen.

Brittle fracture analysis of the offset-crack DCDC specimen

Applications of fracture mechanics in the strength analysis of ceramic materials have been lately studied by many researchers. Various test specimens have been proposed in order to investigate the fracture resistance of cracked bodies under mixed mode conditions. Double Cleavage Drilled Compression (DCDC) specimen, with a hole offset from the centerline is a configuration that is frequently used in subcritical crack growth studies of ceramics and glasses. This specimen exhibits a strong crack path stability that is due to the strongly negative T-stress term. In this paper the maximum tensile stress (MTS) criterion is employed for investigating theoretically the initiation of brittle fracture in the DCDC specimen under mixed mode conditions. It is shown that the T-stress has a significant influence on the predicted fracture load and the crack initiation angle. The theoretical results suggest that brittle fracture in the DCDC specimen is controlled by a combination of the singular stresses (characterized by KI and KII) and the non-singular stress term, T-stress.

Effect of aluminum ions on intrinsic sub-critical crack growth in metaphosphate glasses

Sub-critical crack growth in various kinds of metaphosphate glasses was investigated by using DCDC (Double Cleavage Drilled Compression) technique. The crack growth measurements were only being made in Region III, or in an inert environment. In order to evaluate intrinsic crack growth behaviors in Region III, crack propagation tests were performed in dehydrated heptane, and the crack velocity, v, was plotted as a function of the stress intensity factor, K I. Fracture toughness of glass was also estimated from a stress intensity factor at a given crack velocity. For binary metaphosphate glasses (50MO · 50P 2O 5, M = Zn, Mg, Ca, Ba), fracture toughness increases in the order of Mg > Ca > Zn > Ba. However, the slope of K I– v curve is almost unchanged. In the case of aluminum containing metaphosphate glasses, with increasing aluminum content, fracture toughness increases and the slope of K I– v curve becomes smaller, regardless of the type of divalent cations in glass. It is concluded that an addition of aluminum ions into metaphosphate glass results in both high toughness and easy fatigue. In addition, the structural role of aluminum ions on the intrinsic sub-critical crack growth is discussed in terms of the models of atomistic bond rupture.

In-situ crack propagation observation of a particle reinforced polymer composite using the double cleavage drilled compression specimens

In this study, we investigate the feasibility of in-situ crack propagation by using a double cleavage drilled compression (DCDC) specimen showing a slow crack velocity down to 0.03 mm/s under 0.01 mm/s of displacement control. Finite element analysis predicted that the DCDC specimens would show at least 4.3 fold delayed crack initiation time than conventional tensile fracture specimens under a constant loading speed. Using DCDC specimens, we were able to observe the in-situ crack propagation process in a particle reinforced transparent polymer composite. Our results confirmed that the DCDC specimen would be a good candidate for the in-situ observation of the behavior of particle reinforced composites with slow crack velocity, such as the self-healing process of micro-particle reinforced composites.

A method to evaluate interfacial fracture energy on a fibre/matrix interface

A double cleavage drilled compression (DCDC) specimen was analysed using the boundary element method. The DCDC specimen of FRP composites was proposed and used to evaluate the interfacial behaviour and fracture energy in model composites of carbon fibre reinforced polymer (CFRP). As a result, it was confirmed that the DCDC specimen had the mode I stress distribution for the hole offsetting displacement of b = 0, in which the specimen configuration was symmetrical, while it had the mixed-mode stress distribution for b = 0. The approach of calculating the interfacial fracture energy was established using both the analysis and experiments. Furthermore, the bridging fibre DCDC specimen was proposed and the effect of bridging fibres on the loading phase was made clear. It was shown that the DCDC test was a useful method to evaluate the interfacial behaviour of fibre/matrix in composites.

Fatigue resistance of silane-bonded epoxy/glass interfaces using neat and rubber-toughened epoxies

The influence that the energy absorbing ability of an epoxy has on the cyclic fatigue resistance of a silane-bonded epoxy/glass interface in moist air was studied using the double cleavage drilled compression (DCDC) test. The material properties of two epoxies with similar chemical structures were controlled through the manipulation of the molecular weight between cross-links, Mc, of the epoxy network. Two rubber-toughened epoxies with different nominal particle sizes (10–40 μm and 1–2 μm) were fabricated by adding a liquid butadiene/acrylonitrile copolymer to the epoxy resins. Mixtures of the silane-coupling agents 3-aminopropyltriethoxysilane (3-APES) and propyltriethoxysilane (PES) were used to treat the glass substrate in order to control the number of covalent bonds between epoxy and the glass. 3-APES has the ability to form primary bonds with both the epoxy and the glass, while PES forms primary bonds with only the glass. Experimental results showed that the manipulation of Mc had little effect on the cyclic fatigue resistance of the epoxy/glass interface. However, incorporation of rubber particles gave a significant improvement in the fatigue resistance. The rubber particles allowed the microscopic, non-linear deformation mechanisms of cavitation and shear yielding to dissipate energy during fatigue crack growth. Smaller particles gave the greatest improvement to fatigue resistance; about a 75% improvement compared to the neat (non-modified) epoxy. Adjustment of the number of silane bonds between the neat epoxies and the glass had little effect within experimental scatter on the fatigue resistance of the interfaces, suggesting that the energy dissipated through the breaking of bonds at the interface was insignificant compared to the energy dissipated through plastic and other inelastic deformation mechanisms in the epoxy.

Effect of oxidation treatment on the crack propagation rate of aerogels

Typical silica aerogels obtained by alcohol supercritical drying are hydrophobic. After a low temperature heat treatment below 400°C, they become hydrophilic. The temperature of this heat treatment may increase the network connectivity by establishing new siloxane bonds. On the microscopic scale, this process induces a very small shrinkage during which the silica backbone strengthens and approaches that of pure porous silica. Silica aerogels, whatever the nature of their surface, hydrophobic or hydrophilic, exhibit a stress corrosion effect as previously reported. A comparison of the subcritical crack growth rates of differently heat treated aerogels is given. The experimental investigations are carried out under a controlled moisture of 50% RH using the double cleavage drilled compression (DCDC) technique. The crack length is optically measured within the range 10 −10– 10 −5 m s −1 . For a given stress intensity factor K I, we observe in the stress corrosion domain that hydrophobic aerogels display a very low crack rate. This rate increases with the amount of surface silanols. For higher oxidation temperatures, the number of surface silanols decreases inducing a lowering of the crack rate.

Further analysis of the DCDC specimen with an offset hole

The results of He et al. (1995) for the Double Cleavage Drilled Compression (DCDC) specimen are extended to cover the case where both the hole and crack are offset from the centerline of the specimen. The effect of the thickness of an adhesive layer on the value of the energy release is also investigated. The applicability of the results to experimental studies is presented.