Size Of Fracture Process Zone Research Articles

Size Effect in Thermally Damaged Concrete

Detailed experimental observations and numerical simulations are presented for the evaluation of residual properties of high-strength concrete specimens after exposure to high temperatures. Heated and nonheated notched four-point bending specimens were tested at ambient conditions approximately 1 month after exposure to the high temperature. Residual strength and post-peak response were monitored using a closed-loop load frame, and the fracture process zone was observed using Electronic Speckle Interferometry. The symmetric over-nonlocal formulation of a microplane model was used for interpreting the experimental investigation. The size-effect results were used to identify the true tensile strength and the initial fracture energy corresponding to the peak and the initial post-peak slope of a linear cohesive crack law. This study reveals that the material ductility increases with the thermal damage, which is explained by the increase of the fracture process zone size and the characteristic length.

Study on Interfacial Crack Propagation and Fracture between Embedded Steel and HSHPC

Steel reinforced high strength and high performance concrete (SRHSHPC) specimens were experimented to study the mechanical behaviors between steel and concrete interface. In experiment, interfacial bond softening process was observed, which can be explained in terms of damage along the interface, leading to progressive reduction of shear transfer capability between steel and high strength and high performance concrete (HSHPC). In this paper, bond softening process along the interface is considered in the analysis of crack-induced debonding. Interfacial bond-slip mechanism between steel and HSHPC is studied in detail based on fracture mechanics. With the help of acoustic emissions technology, the crack propagation in the interlayer was observed, thus the interfacial crack propagation and fracture model is set up. Under the assumption that the interlayer is weak concrete compared with concrete matrix, the stress field as well as displacement field around the crack tip is deduced. The characteristics of interfacial fracture process are discussed and a model for interfacial fracture process zone is built up. With this model, the size of fracture process zone can be derived. At last, the influence of the fracture process zone on interfacial fracture toughness is determined using critical fracture toughness. All these may contribute to improvement of theory for SRHSHPC composite structure.

Influence of paste volume on shrinkage cracking and fracture properties of self-compacting concrete

Self-compacting concrete (SCC) mixtures are usually designed with higher volumes of paste than vibrated concrete mixtures. The results reported in this paper come from a study of nine SCC concrete mixtures. Volume of paste was varied between 291 and 457 l/m3. One of the mixtures had already been used in a large scale test, and the others were designed by varying several parameters of the reference concrete mixture. Mechanical properties, shrinkage, fracture parameters and fracture process zone (FPZ) size were measured. Fracture behavior was characterized by means of three-point bending tests and acoustic emission analysis. From the experimental results, increasing the volume of paste has a restricted effect on strength, unless water content varies. Strength, elastic modulus and fracture resistance slightly decrease with an increase in paste content. Volume of paste causes an increase in shrinkage and cracking due to shrinkage. Fracture and acoustic emission analysis show that increasing the volume of paste tends to make SCC more brittle.

On the fracture resistance of adhesively jointing structures

The interface toughness of adhesively bonded structural members is one of the critical parameters for adhesive joint design. It is often assumed that the joint toughness is a material constant so that its value can be obtained from fracture tests of simple geometries such as DCB for Mode-I, ENF for Mode-II, using linear elastic fracture mechanics (LEFM). However, the LEFM assumption of point-wise crack-tip fracture process is overly simplistic and may cause significant error in interpreting fracture test data. In this paper, the accuracy and applicability of various traditional beam-bending-theory based methods for fracture toughness evaluation, such as simple beam theory (SBT), corrected beam theory (CBT) and experimental compliance method (ECM), were assessed using the cohesive zone modelling (CZM) approach. It was demonstrated that the fracture process zone (FPZ) size has profound influence on toughness calculation and unfortunately, all the classic beam-bending theories based methods fail to include this important element and are erroneous especially when the ratio of crack length to FPZ size is relatively small (<5.0). It has also been demonstrated that after the FPZ size is incorporated into simple beam formulations, they provide much improved evaluation for fracture toughness. Formulation of first order estimate of FPZ size is also given in this paper.

Modeling and simulation of intersonic crack growth

Intersonic crack growth has been studied using an interfacial fracture model in which an additional material phase within a bonding layer is proposed to describe the failure behavior of the interface. In this material phase, a strain gradient based damage model is applied with a built-in cohesive law, which is governed by an material intrinsic length scale that bridges the mechanisms that operate at continuum mechanics scale and at smaller scales. Simulations of the intersonic crack growth experiments ( Rosakis et al., 1999; Rosakis, 2002) have been performed with varying material length scales and other parameters. The study is focused on two subjects: (1) the process of decohesion-induced cracking, explaining fracture process zone initiation and propagation as well as the corresponding contact mechanisms; (2) propagation speed, investigating the effects of length scales and loading parameters. The simulations reveal that a fracture process zone initiates first and extends with a speed faster than shear wave speed. After initiation, the crack speed exhibits oscillations with an average value between c s 2 and c l, where c s and c l refer to shear wave and dilatation wave speeds, respectively. In such a quasi-steady-state propagation, the crack opening profiles exhibit a time-invariant profile, while the fracture process zone size and decohesion energy remain constant. Contact between the crack faces is taken into account in the numerical simulations. A contact zone behind the crack tip has been captured which represents a self-healing-like mechanism. The leading edge of both the fracture process zone and the contact zone may cause strong shocks. When the average crack propagation speed approaches the supersonic region, two stress shocks radiate from the crack tip, corresponding to shear and dilatation wave radiation, respectively. The simulation results demonstrate that length and time scales play vital roles during crack propagation. Here the length scales refer to the bonding layer thickness and the material’s intrinsic length that governs energy dissipation during failure; whereas the time scales refer to the effects of material strain rate dependence, material failure speed, and wave propagation properties. A parameter R s, expressed as the ratio of material shear strength and the applied stress that is calculated from the remote imposed displacement boundary condition, is proposed to scale crack speed. Intersonic propagation occurs when R s is greater than a threshold value. The numerical computations are compared with experiments ( Rosakis et al., 1999; Rosakis, 2002) and the theoretical solution [Philos. Mag., A, in press], which demonstrates the trend that crack propagation is unstable in the open speed interval between c s and κ v c s ( 2 ⩽κ v <c l /c s ) whereas it is stable when the speed lies in the close interval between κ v c s and c l. The coefficient κ v is a function of material length scale, strain rate sensitivity, and boundary conditions. The moving particle finite element method, a newly developed meshfree method, and the pinball contact algorithm are applied in the numerical analysis.

Crack blunting and the strength of soft elastic solids

When a material is so soft that the cohesive strength (or adhesive strength, in the case of interfacial fracture) exceeds the elastic modulus of the material, we show that a crack will blunt instead of propagating. Large–deformation finite–element model (FEM) simulations of crack initiation, in which the debonding processes are quantified using a cohesive zone model, are used to support this hypothesis. An approximate analytic solution, which agrees well with the FEM simulation, gives additional insight into the blunting process. The consequence of this result on the strength of soft, rubbery materials is the main topic of this paper. We propose two mechanisms by which crack growth can occur in such blunted regions. We have also performed experiments on two different elastomers to demonstrate elastic blunting. In one system, we present some details on a void growth mechanism for ultimate failure, post–blunting. Finally, we demonstrate how crack blunting can shed light on some long–standing problems in the area of adhesion and fracture of elastomers.

T-stress, mixed-mode stress intensity factors, and crack initiation angles in functionally graded materials: a unified approach using the interaction integral method

For linear elastic functionally graded materials (FGMs), the fracture parameters describing the crack tip fields include not only stress intensity factors (SIFs) but also T-stress (nonsingular stress). These two fracture parameters are important for determining the crack initiation angle under mixed-mode loading conditions in brittle FGMs (e.g. ceramic/ceramic such as TiC/SiC). In this paper, the mixed-mode SIFs and T-stress are evaluated by means of the interaction integral, in the form of an equivalent domain integral, in combination with the finite element method. In order to predict the crack initiation angle in brittle FGMs, this paper makes use of a fracture criterion which incorporates the T-stress effect. This type of criterion involves the mixed-mode SIFs, the T-stress, and a physical length scale r c (representative of the fracture process zone size). Various types of material gradations are considered such as continuum models (e.g. exponentially graded material) and micromechanics models (e.g. self-consistent model). Several examples are given to show the accuracy and efficiency of the interaction integral scheme for evaluating mixed-mode SIFs, T-stress, and crack initiation angle. The techniques developed provide a basic framework for quasi-static crack propagation in FGMs.

A model material approach to the study of fracture process zone of quasi-brittle materials

A new approach to study the fracture of quasi-brittle materials is introduced: the design and testing of model materials. By model material is understood a material with enlarged microstructure and which material parameters, such as stacking and mechanical properties of particles and cohesion force, can be fully controlled. In this paper a first example to the model materials approach is presented, consisting in 5 mm steel particles bonded in a precise stacking with an epoxy-based glue. It is shown how it is possible to correlate the different fracture mechanisms and ultimate peak load of the model material to the particle pair force and to the fracture process zone size. It is also seen how a quasi-brittle behaviour is produced in the presence of mechanisms that induced the crack to shift fracture planes, that is, in presence of energy dissipative mechanisms.

Evaluation of fracture toughness of ceramic matrix composites using small specimens

Ceramic matrix composites (CMC) are being developed for high temperature utilization in aerospace and other industrial application. They offer several attractive features including high strength and modulus, improved fracture toughness, light weight, low thermal expansion coefficient and high thermal conductivity which contribute to good thermal shock resistance and high temperature stability in chemical and oxidative environments. Though the enhancement of fracture toughness is one of key issues for the development of these materials, the standardized evaluation method for the characterization of fracture toughness has not been established yet. Miniaturization of the test specimen for these tests has been also considered to be one of the most necessary issues because of the high cost of materials and the restriction of experimental environments. In this study, the influences of specimen size on the fracture resistance properties of plain-woven (P/W) Carbon/Carbon and Tyranno-LoxM/SiC composite were investigated. The fracture toughness tests with the unloading–reloading sequences were conducted with the compact tension specimens of different thicknesses and widths. The initiation fracture toughness J Q of both materials increased with increasing of specimen thickness. It seems that interlayer frictional sliding between layered fabrics is one of energy dissipating mechanism in these materials. The initiation fracture toughness, J Q, of both materials also increased with increasing of specimen width. The specimen width and the fabric condition affect the size of fracture process zone in 2D woven CMC.

Mode I and mode II crack tip asymptotic fields with strain gradient effects

The strain gradient effect becomes significant when the size of fracture process zone around a crack tip is comparable to the intrinsic material lengthl, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dominant strain field is irrotational. For mode I plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist simultaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode II plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode II plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode I and mode II, because the present theory is based only on the rotational gradient of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient.

Prediction of intrinsic fracture toughness for brittle materials from the apparent toughness of notched-crack specimen

In this investigation, fracture process zone model is used to establish a new relationship to predict the intrinsic fracture toughness from the apparent fracture toughness of a notched-crack specimen. The parameters needed in the proposed model are very rare, such as, the fracture process zone size of materials, the notch radius. Specimens made up of two kinds of polycrystalline alumina and one soda-lime glass with notch radii as small as a few micrometer are used to verify the predictions of this model. Besides, the results also show that fracture toughness of ceramics decreases with the decreasing of notch root radius. Under condition of the radius of crack tip is not greater than the averaged grain size, the apparent toughness can be approximately regarded as the fracture toughness of the materials.

The damage process zone characteristics at crack tip in concrete

This paper presents a comprehensive derivation of fracture process zone size which closely parallels similar work in fracture of metals and anisotropic solids, but is adapted to conrete. Some nonlinear mechanics models of concrete materials will be discussed by using uniaxial stress assumptions. For uniaxial stress assumption, energy model and fracture model will be presented for nonlinear softening models. Finally, we make a comparison with those models.

Scaling of quasibrittle fracture: asymptotic analysis

Fracture of quasibrittle materials such as concrete, rock, ice, tough ceramics and various fibrous or particulate composites, exhibits complex size effects. An asymptotic theory of scaling governing these size effects is presented, while its extension to fractal cracks is left to a companion paper (1) which follows. The energy release from the structure is assumed to depend on its size , on the crack length, and on the material length governing the fracture process zone size. Based on the condition of energy balance during fracture propagation and the condition of stability limit under load control, the large-size and small-size asymptotic expansions of the size effect on the nominal strength of structure containing large cracks or notches are derived. It is shown that the form of the approximate size effect law previously deduced (2) by other arguments can be obtained from these expansions by asymptotic matching. This law represents a smooth transition from the case of no size effect, corresponding to plasticity, to the power law size effect of linear elastic fracture mechanics. The analysis is further extended to deduce the asymptotic expansion of the size effect for crack initiation in the boundary layer from a smooth surface of structure. Finally, a universal size effect law which approximately describes both failures at large cracks (or notches) and failures at crack initiation from a smooth surface is derived by matching the aforementioned three asymptotic expansions.

Tensile cracks in polycrystalline ice under transient creep: Part II — Numerical simulations

Abstract This paper discusses predictions of a numerical model presented in the companion paper (Nanthikesan and Shyam Sunder, 1995) to analyze tensile cracks in polycrystalline ice undergoing transient creep. The numerical model is based on the internal state variable constitutive theory of transient creep in ice developed by Shyam Sunder and Wu (1989a,b, 1990). The finite element model uses the boundary layer approach of Rice (1968), in conjunction with a mid-point crack-tip element and reduced integration, to simulate the asymptotic stress and deformation fields in the vicinity of the crack tip, including incompressible creep deformations. The problem of a stationary, traction-free, tensile (mode I) crack is analyzed to predict the size, shape and time evolution of the creep-dominated fracture process zone surrounding the crack-tip. The numerical simulations quantify the effects of transient creep, material strain hardening, fabric anisotropy, loading rate, temperature, and finite fracture test-specimen boundary on the development of the creep zone. A range of stress-intensity rates from 1 to 100 kPa m 1 2 s−1 and temperatures from −5° to −25°C is considered in the simulations. The results from a comprehensive numerical simulation study show that: (i) transient creep increases the creep zone size by more than an order of magnitude over that for a power-law creeping material, i.e., about 40 times for the isotropic, equiaxed granular ice tested by Jacka (1984); (ii) material strain hardening significantly affects the creep zone size, i.e., the creep zone for the transversely-isotropic columnar-grained ice tested by Sinha (1978), with the crack loaded in the plane of isotropy, is about 4 times smaller than that for the granular isotropic ice; (iii) fabric anisotropy increases the size of the creep zone by a factor of at least two for cracks in the transversely-isotropic, columnar-grained ice loaded in the plane of isotropy; (iv) the Riedel and Rice (1980) equation, which was derived for an isotropic power-law creeping material subjected to a suddenly applied constant stress-intensity, overestimates the creep zone size by a factor of 4.2 for a constant stress-intensity rate loading; and (v) as the crack size increases, linear elastic fracture mechanics becomes increasingly applicable at lower loading rates and higher temperatures.

Modelling the fissuring flat-fracture mode of crack growth in Zr-2.5Nb Candu pressure-tube material

Modelling of the fissuring mode of fracture in Candu pressure-tube material and, in particular, Stage 1 crack growth (essentially flat Jr curve) as observed in some irradiated compact toughness specimens, is reported. A preliminary attempt has been made at modelling the characteristics of the fracture process zone associated with a crack that tunnels at the specimen mid-section. Based on the experimentally determined Jr curve, both the fracture-process zone size and the crack opening displacement at the trailing edge of the zone have been predicted, and their values are seemingly not unreasonable. The initial considerations enable specific issues to be highlighted which need to be addressed before a complete picture is obtained of the fissuring mode of crack growth. A theoretical analysis has also shown that the non-tunnelling material at the specimen side surfaces exerts very little restraint on the cumulative (tunnelling) mode of crack propagation, a prediction that is consistent with the experimental finding that Stage 1 crack growth in irradiated material is associated with an essentially flat Jr curve.

Size effect method for determining fracture energy and process zone size of concrete : Shah, S P Mater StructV23, N138, Nov 1990, P461–465

Size effect method for determining fracture energy and process zone size of concrete : Shah, S P Mater StructV23, N138, Nov 1990, P461–465

Size-effect method for determining fracture energy and process zone size of concrete

Size-effect method for determining fracture energy and process zone size of concrete