Crack Opening Displacement Profiles Research Articles

Analytical model for near-crack debonding in fiber-reinforced polymer composite-overlaid metallic plates with a central crack

Extensive research has been undertaken on the use of fiber-reinforced polymer (FRP) in the strengthening of fatigue-damaged and fatigue-prone civil engineering metallic structures. Evaluation of the static load-bearing capacity and fatigue life of the so-strengthened structures necessitates the accurate prediction of the stress intensity factor (SIF) for an FRP-overlaid crack in a metallic structure. This paper first presents a new analytical model for predicting the near-crack interfacial debonding process and its effect on the SIF of a centrally cracked metallic plate that is bonded on both sides with an FRP overlay. The stress distributions in both the overlays and the metallic plate, the interfacial shear stress distribution, the crack opening displacement profile, and the SIF can all be found without the need for any a priori assumption of the near-crack interfacial debonding process/pattern. The accuracy of the analytical model is evaluated with both finite element predictions and experimental data. The analytical model is then used to advance our understanding of the mechanisms of near-crack interfacial debonding, including both the initiation and propagation of debonding, as well as the effect of near-crack debonding on the SIF. It should be noted that while the study was conducted with explicit reference to metallic plates bonded with FRP overlays, the analytical model is applicable to combinations of other materials as long as the substrate plate material is isotropic, and both components remain linear-elastic during the loading process.

Study on crack propagation of functionally graded ultra-high performance cementitious composite

This study investigates the damage process and crack propagation of functionally graded ultra-high-performance cementitious composite (FGUHPCC) with different layers (two and three layers) and fibers types (steel and PVA) through four-point bending test. The evolution process of surface displacement and strain of the sample was analyzed by digital image correlation (DIC) technology, and the influence of the top, middle and bottom layers of FGUHPCC on the damage pattern are also investigated by RFPA3D program. The results indicate that functionally graded design improves the equivalent flexural strength and deflection capacity of the specimens compared with the UHPCC with single layer design. FGUHPCC with three layers and mixed steel and polyvinyl alcohol fibers exhibited best flexural behavior. According to the recorded DIC data and corresponding analyses, the crack opening displacement (COD) profile of functionally graded design with three layers is mutable and nonlinear, and the maximum crack propagation speed is 0.096 L/s, which is the lowest compared with other tested specimens, and the largest crack area ratios are about 0.04% and 0.147% at LOP and MOR, respectively. Based on RFPA3D results, with the change of fiber content, the cumulative AE energy growth rate (k) of bottom layer is about 2.7 times and 1.5 times of that of the middle layer and the top layer, respectively.

Usage of compact compression specimens to determine non‐linear fracture parameters of concrete

AbstractUp to now, the compact compression specimens (CCS) have only been used to estimate the fracture toughness parameter of cement‐based materials. In the study, the linear elastic fracture mechanics formulae of CCS, namely, the universal weight functions with four terms, KI (stress intensity factor), CMOD (crack mouth opening displacement), and COD (crack opening displacement) profile were, therefore, derived using the finite element method. To investigate the extent to which CCS tests could model the non‐linear fracture behaviour of concrete, 11 series of tests in the literature were subsequently examined for the effective crack models: the two‐parameter model, the size effect model, and the double‐K model. Two prediction formulae based on previous test data were proposed to estimate unstable fracture toughness and initiation fracture toughness of concrete. The results of CCS test‐based non‐linear fracture mechanics look viable and very promising.

Experimental investigation of the process of corrosion-caused cover cracking

Corrosion-caused cover cracking can lead to the serious deterioration of reinforced concrete (RC) structures. However, only a few experimental studies in the literature have examined the entire cracking process of specimens with a realistic configuration that consists of both the concrete cover and concrete core. Herein, the mechanism and process of cover cracking are experimentally investigated for cover and core specimens by using accelerated corrosion tests together with digital image correlation. The entire process of corrosion-caused cover cracking is experimentally recorded. The phenomenon of the rotation of the cover is first observed. Furthermore, the direction of the crack propagation, crack opening displacement (COD) profiles and the concrete expansion at the steel/concrete interface are measured. The relationship between total rust and the rust that causes expansion pressure on the surrounding concrete is examined. The test results are then used to validate a previously proposed elastic-body-rotation model for simulating cover cracking.

Evaluation of tension softening curve of concrete at low temperatures using the incremental displacement collocation method

The three-point bending tests of concrete beams at different temperatures (20 °C, 0 °C, −20 °C, and −40 °C) were carried out by using a low-temperature fracture test system. The digital image correlation technique was utilized to measure the surface displacement and strain fields of the specimens. The crack characteristics, including the crack propagation length and the crack opening displacement profile were determined. The tension softening curves (TSCs) of concrete were obtained using the incremental displacement collocation method. The developed TSCs were verified through the comparisons of the displacements determined by finite element method and by clip gauge as well as the fracture energy. In addition, based on the double-K fracture criterion, the deviations of two fracture toughness were analyzed, and again the accuracy of the TSCs was verified. Finally, the results of characteristic length and damage scale were also presented in this paper.

Fracture behavior of nuclear graphite under three-point bending tests

Three-point bending tests are performed on center-notched graphite beams to study the fracture properties of IG11 graphite. Electronic speckle pattern interferometry (ESPI) is used to measure the full-field deformation of the graphite beams. A clip gauge is used to measure the crack mouth opening displacement (CMOD) of the beams, which validates the ESPI measurements. In addition, finite element (FE) analysis is performed by using the ABAQUS code coupled with the extended FE method to simulate the growth of cracks in graphite. A combined stress-energy based fracture criterion, specifically, damage for traction separation laws based on maximum principal stress damage initiation and energy based damage evolution with linear softening is applied. The numerical results are compared with the experimental results which show exceptional agreement, thus confirming the accuracy of the FE model. The fracture toughness KIc, fracture energy GF, peak load Pmax and critical displacements at the peak load of each specimen are determined. From the displacement contours measured by ESPI, the positions of the neutral axis and crack opening displacement (COD) profiles at different loading levels are estimated. From the phase maps, the changes in the fracture process zone (FPZ) are analyzed and the size of the FPZ is determined. The strain contours at different loadings indicate that the material near the crack tip experiences biaxial tensile stress.

The effect of residual stress on whisker reinforcements in SiCw-Al2O3 composites during cooling

The effect of residual stress on whisker reinforcements in SiCw-Al2O3 composites from 293 K to 77 K was investigated. The fracture toughness of SiCw-Al2O3 composites measured at 77 K was ∼26% higher than that at 293 K. The calculated compressive stress of SiC whiskers at 77 K was ∼600 MPa, and the local stress distribution is demonstrated by in-situ Raman spectra and fluorescence spectra. R-Curve behaviors and crack opening displacement profiles were determined to compare the effect of residual stress on crack bridging at different temperatures. The experimental results verified that crack bridging was enhanced by residual stress at 77 K, which made the SiCw-Al2O3 composite to be a promising material for cryogenic applications.

Determination of Double-K Fracture Parameters of Concrete Using Split-Tension Cube: A Revised Procedure

This paper presents a revised procedure for computation of double-K fracture parameters of concrete split-tension cube specimen using weight function of the centrally cracked plate of finite strip with a finite width. This is an improvement over the previous work of the authors in which the determination of double-K fracture parameters of concrete for split-tension cube test using weight function of the centrally cracked plate of infinite strip with a finite width was presented. In a recent research, it was pointed out that there are great differences between a finite strip and an infinite strip regarding their weight function and the solution of infinite strip can be utilized in the split-tension specimens when the notch size is very small. In the present work, improved version of LEFM formulas for stress intensity factor, crack mouth opening displacement and crack opening displacement profile presented in the recent research work are incorporated. The results of the double-K fracture parameters obtained using revised procedure and the previous work of the authors is compared. The double-K fracture parameters of split-tension cube specimen are also compared with those obtained for standard three point bend test specimen. The input data required for determining double-K fracture parameters for both the specimen geometries for laboratory size specimens are obtained using well known version of the Fictitious Crack Model.

Surface toughness of silicon nitride bioceramics: II, Comparison with commercial oxide materials

Raman microprobe-assisted indentation, a micromechanics method validated in a companion paper, was used to compare the surface toughening behaviors of silicon nitride (Si3N4) and alumina-based bioceramics employed in joint arthroplasty (i.e., monolithic alumina, Al2O3, and yttria-stabilized zirconia (ZrO2)-toughened alumina, ZTA). Quantitative assessments of microscopic stress fields both ahead and behind the tip of Vickers indentation cracks propagated under increasing indentation loads were systematically made using a Raman microprobe with spatial resolution on the order of a single micrometer. Concurrently, crack opening displacement (COD) profiles were monitored on the same microcracks screened by Raman spectroscopy. The Raman eye clearly visualized different mechanisms operative in toughening Si3N4 and ZTA bioceramics (i.e., crack-face bridging and ZrO2 polymorphic transformation, respectively) as compared to the brittle behavior of monolithic Al2O3. Moreover, emphasis was placed on assessing not only the effectiveness but also the durability of such toughening effects when the biomaterials were aged in a hydrothermal environment. A significant degree of embrittlement at the biomaterial surface was recorded in the transformation-toughened ZTA, with the surface toughness reduced by exposure to the hydrothermal environment. Conversely, the Si3N4 biomaterial experienced a surface toughness value independent of hydrothermal attack. Crack-face bridging thus appears to be a durable surface toughening mechanism for biomaterials in joint arthroplasty.

Fatigue crack growth in CFRP-strengthened steel plates

In this paper fatigue crack growth in steel plates reinforced by using carbon fiber reinforced (CFRP) strips is investigated from the experimental, numerical and analytical point of view. Single edge notched tension (SENT) specimens were strengthened with different reinforcement configurations and tested at a stress ratio R of 0.4. Different initial damage levels were considered and the experimental results showed that the reinforcement application can effectively reduce the crack growth rate and significantly extend the fatigue life. Numerical models (finite elements) were also developed to evaluate the stress intensity factor (SIF) and the crack opening displacement (COD) profile. Based on the numerical results, an analytical model was proposed to predict the fatigue crack growth rate and the fatigue crack growth curves. The analytical results are validated by comparing the fatigue crack growth curves to the experimental ones.

How Does Crack Bridging Change at Cryogenic Temperatures?

The crack bridging behaviors of silicon nitride (Si3N4) ceramics based on the advancing cracks have been evaluated at cryogenic temperatures in contrast with those happened at ambient temperatures. R‐Curve behavior of Si3N4 ceramics was determined to compare the cumulative effect of bridging at 77 and 293 K. The detailed changes in crack morphologies and crack opening displacement profiles at different temperatures were investigated. The bridging stress maps around a bridging ligament were recorded by in situ Raman spectroscopy. It was found that the highest tensile stress measured at 77 K (~1.0 GPa) is much higher than that at 293 K (~0.7 GPa). The experimental results suggested that Si3N4 ceramics at cryogenic temperatures possessed a higher probability of crack bridging with a higher closing force, which could make them a promising candidate for cryogenic applications.

Tension softening curves of plain concrete

The tension softening curves (TSCs) of plain concrete with compressive strengths varying between 40 and 90MPa were estimated by performing three-point bending tests on pre-notched beams. Crack evolution and full-field deformation in the beams were measured using the electronic speckle pattern interferometry technique. The crack characteristics, including the crack opening displacement profiles, the width of the fracture process zone and the length of the crack, were evaluated. By using a newly developed incremental displacement collocation method, the TSCs of plain concrete were determined. To facilitate the use of TSCs by commercial finite element packages, the estimated TSCs were simplified to bilinear and exponential curves, and the related parameters were determined.

Optimization of Digital Image Correlation for High-Resolution Strain Mapping of Ceramic Composites

Digital image correlation (DIC) is assessed as a tool for measuring strains with high spatial resolution in woven-fiber ceramic matrix composites. Using results of mechanical tests on aluminum alloy specimens in various geometric configurations, guidelines are provided for selecting DIC test parameters to maximize the extent of correlation and to minimize errors in displacements and strains. The latter error is shown to be exacerbated by the presence of strain gradients. In a case study, the resulting guidelines are applied to the measurement of strain fields in a SiC/SiC composite comprising 2-D woven fiber. Sub-fiber tow resolution of strain and low strain error are achieved. The fiber weave architecture is seen to exert a significant influence over strain heterogeneity within the composite. Moreover, strain concentrations at tow crossovers lead to the formation of macroscopic cracks in adjacent longitudinal tows. Such cracks initially grow stably, subject to increasing app lied stress, but ultimately lead to composite rupture. Once cracking is evident, the composite response is couched in terms of displacements, since the computed strains lack physical meaning in the vicinity of cracks. DIC is used to identify the locations of these cracks (via displacement discontinuities) and to measure the crack opening displacement profiles as a function of applied stress.

High resolution analysis of opening and sliding in fatigue crack growth

The use of digital image correlation analysis during fatigue crack growth (FCG) of polycrystalline and [1 1 1] oriented single crystal specimens of 316L stainless steel allows for the investigation of mixed mode crack propagation in the vicinity of the crack tip. This technique offers significant benefit in addressing crack closure at the microscale compared to the large body of work studying this phenomenon at the macroscale. Understanding of FCG behavior relies on the sliding (mode II) details which can be rather complicated. In this study, the mode I (opening) and mode II (sliding) mechanisms are differentiated within the single crystal specimens for slanted cracks. Further, crack opening displacement profiles are obtained in mode I and mode II, which are used to quantify crack closure in each specimen. Finally, the irreversible strain within the plastic zone ahead of the crack tip is measured during crack propagation. The results show that [1 1 1] oriented single crystal specimen fatigued at R = −1 display the most slip irreversibilities due to reverse dislocation motion leading to dislocation kinks/jogs. As a result, residual stress is diminished at the crack tip thereby resulting in earlier crack opening within the loading cycle.

Finite element analysis of an atomistically derived cohesive model for brittle fracture

In order to apply information from molecular dynamics (MD) simulations in problems governed by engineering length and time scales, a coarse graining methodology must be used. In previous work by Zhou et al (2009 Acta Mater. 57 4671–86), a traction-separation cohesive model was developed using results from MD simulations with atomistic-to-continuum measures of stress and displacement. Here, we implement this cohesive model within a combined finite element/cohesive surface element framework (referred to as a finite element approach or FEA), and examine the ability for the atomistically informed FEA to directly reproduce results from MD. We find that FEA shows close agreement of both stress and crack opening displacement profiles at the cohesive interface, although some differences do exist that can be attributed to the stochastic nature of finite temperature MD. The FEA methodology is then used to study slower loading rates that are computationally expensive for MD. We find that the crack growth process initially exhibits a rate-independent relationship between crack length and boundary displacement, followed by a rate-dependent regime where, at a given amount of boundary displacement, a lower applied strain rate produces a longer crack length. Our method is also extended to larger length scales by simulating a compact tension fracture-mechanics specimen with sub-micrometer dimensions. Such a simulation shows a computational speedup of approximately four orders of magnitude over conventional atomistic simulation, while exhibiting the expected fracture-mechanics response. Finally, differences between FEA and MD are explored with respect to ensemble and temperature effects in MD, and their impact on the cohesive model and crack growth behavior. These results enable us to make several recommendations to improve the methodology used to derive cohesive laws from MD simulations. In light of this work, which has critical implications for efforts to derive continuum laws from MD simulations, it is shown care must be taken when using a similar approach, and effects of ensemble, temperature and strain rate must be considered.

Crack tip fracture toughness of base glasses for dental restoration glass-ceramics using crack opening displacements

The critical stress intensity factor, also known as the crack tip toughness K tip , was determined for three base glasses, which are used in the manufacture of glass-ceramics. The glasses included the base glass for a lithium disilicate glass-ceramic, the base glass for a fluoroapatite glass-ceramic and the base glass for a leucite glass-ceramic. These glass-ceramic are extensively used in the form of biomaterials in restorative dental medicine. The crack tip toughness was established by using crack opening displacement profiles under experimental conditions. The crack was produced by Vickers indentation. The crack tip toughness parameters determined for the three glass-ceramics differed quite significantly. The crack tip parameters of the lithium disilicate base glass and the leucite base glass were higher than that of the fluoroapatite base glass. This last material showed glass-in-glass phase separation. The discussion of the results clearly shows that the droplet glass phase is softer than the glass matrix. Therefore, the authors conclude that a direct relationship exists between the chemical nature of the glasses and the crack tip parameter.

Determination of concrete fracture parameters based on two-parameter and size effect models using split-tension cubes

The notched beam specimens have been commonly used in concrete fracture. In this study, the splitting-cube specimens, which have some advantages – compactness and lightness – compared to the beams, were analyzed for the effective crack models: two-parameter model and size effect model. The linear elastic fracture mechanics formulas of the cube specimens namely the stress intensity factor, the crack mouth opening displacement, and the crack opening displacement profile were first determined for different load-distributed widths using the finite element method. Subsequently, four series of experimental studies on cubic, cylindrical, and beam specimens were performed. The statistical investigations indicated that the results of the split-cube tests look viable and very promising.

Multiple Crack Analysis in Finite Plates

In this study, interactions of multiple cracks in finite rectangular plates are analyzed. A finite plate is treated as a polygon-shaped plate which can be created by contiguous crack segments embedded in an infinite plate forming an enclosed region so there are no true crack tips remaining around the plate. The problem is formulated in terms of integral equations expressed by edge dislocation distributions representing opening displacement profiles for the cracks with both normal and tangential components. To solve this boundary value problem we employ the superposition approach based on the dislocation distributions requiring the determination of crack opening displacement profiles that satisfy the traction- free condition on interior crack faces and the given boundary tractions on four exterior cracks defining the rectangular plate. Applying the method with a new point allocation scheme reducing the number of evaluation points leads to a set of linear algebraic equations in terms of unknown weighting coefficients of opening displacement profiles. These opening displacement profile components are categorized in terms of polynomial terms which are integers and wedge terms which are rational numbers approximated from irrational wedge eigenvalues to evaluate integrals in closed forms. Once the coefficients of opening displacement profile components are obtained, stress and displacement fields on the entire body, as well as stress intensity factors at the crack tips and kinks are calculated. After the accuracy of the method is shown by comparing the results for different sample problems, the strong interactions of multiple cracks in a rectangular plate under various loading conditions are demonstrated with figures and tables.

R-curve modeling for Ni/Al 2O 3 laminates

A metal/ceramic laminate has increased fracture toughness as compared to the ceramic monoliths. The toughness enhancement is controlled by the closure (‘bridging-stresses’) exerted by the metallic bridging layers (‘ligaments’) astride the crack in the ceramic layers. The crack-opening-displacement (COD) carries information on the level and location of these stresses. If the COD profile is known, the bridging-stresses and consequently, the R-curve behavior of the composite can be modeled. In this study, a weight-function-based approach is used to generate the R-curve and is compared with experimental results for Al 2O 3/Ni multilayer laminates.

Stress intensity factor for center-cracked plate with crack surface interference

This paper presents a simple and physically acceptable analysis of stress intensity factor (SIF) for the center-cracked infinite and finite-width plates. The analysis includes the effect of crack surface interference (i.e., the upper and lower crack surfaces are not allowed to overlap) that influences both the SIF at the tension-side crack tip and the crack opening displacement (COD) profile. For an infinite plate, exact solutions are obtained by superimposing the classical (overlapping) solutions. For a finite-width plate, where the SIF solutions cannot be found in closed form, the solutions are carried out numerically. The overlapping SIF solutions from the weight function method are used. An example is given for the case of a finite-width plate under bending. It was found that the overlapping solutions underestimate the stress intensity factor at the tension-side crack tip up to 15%. The analysis results are also compared with the finite element solutions for verification purpose.