Energetic Size Effect Law Research Articles

Fracture toughness testing of metallic materials based on scratch tests

As a crucial parameter for determining a material's resistance to crack propagation, the convenient characterization of fracture toughness has attracted much attention. The scratch test is an alternate method for determining fracture toughness because it does not require notches or pre-existing cracks and only requires a minimal sample volume. In this study, the product of strength and elongation of materials is incorporated into a modified model based on the energy size effect law to calculate the fracture toughness of metallic materials using scratch tests. To validate the proposed model, scratch tests of DP800, 18CrNiMo7-6, 4140, and 4340 are performed to characterize their fracture toughness. The fracture toughness of these four metallic materials determined from scratch tests utilizing the proposed model, Akono's linear elastic fracture mechanics (LEFM) model, Akono's microscopic energetic size effect law (MESEL) model, Hubler's MESEL model, and Liu's MESEL model are compared with the results from a compact tensile test or single edge notched beam test. Our results indicate that our modified approach is applicable to metallic materials. The proposed model could be reduced to the linear elastic fracture mechanics model. This study offers an efficient way of characterizing the fracture toughness of materials using the scratch method.

Size Effect on FRP External Reinforcement and Retrofit of Concrete Structures

The size effect on the strength of reinforced concrete (RC) beams flexurally strengthened by surface bonded sheets of fiber-reinforced polymer (FRP) is studied. As the failure is neither ductile nor brittle, but quasibrittle, occurring after stable growth of large cracks with large damage zones, the transitional size effect governed by the energetic size effect law (SEL) must be expected, which the present analysis confirms. Owing to scarcity of size effect experimental data, finite element (FE) analysis is used. A powerful microplane damage constitutive model M7 for concrete, coupled with the crack band model to suppress spurious mesh sensitivity, is calibrated by fitting the existing test data to FRP-strengthened RC specimens of diverse types, and consequently is trusted to simulate the size effect. The analysis captures the debonding near the concrete–FRP interface starting at midspan or at the end of the FRP sheet. It also captures the debonding between adjacent concrete shear cracks, and the delamination of concrete cover. The causes of these different delamination modes are explained. Simple beam-type formulas, in which the size characteristic is not the beam depth but the length of the shear span, are proposed and validated by FE results. The use of single-lap shear tests to determine the bond strength is critically discussed. Finally, a good fit of a few existing limited test data on the size effect of FRP-strengthened specimens is demonstrated.

Measurement of fracture toughness of copper via constant-load microscratch with a spherical indenter

Fracture toughness can be measured by microscratch test from objective force and depth measurement, which is much convenient than indentation approach and conventional means, since initial notch or pre-crack is not required. Micro-scratch test was conducted on copper under a spherical probe of radius 105 μm and constant applied normal load with the aim of characterizing fracture toughness of copper by sliding technique with a sphere. Scratch variables such as normal load, lateral load, friction coefficient, and penetration depth were analyzed, and different methodologies for calculating fracture toughness were compared. Linear elastic fracture mechanics was found to be inapplicable to scratch of elastic-plastic material with sufficient plasticity under a spherical probe, while energetic size effect law can be successfully applied to characterize fracture toughness by microscratch test with a sphere abrading metallic material.

Critique of critical shear crack theory for fib Model Code articles on shear strength and size effect of reinforced concrete beams

The size effect of Muttoni et al.'s critical shear crack theory (CSCT) is shown to be quite close (with differences up to 15%) and asymptotically identical to the energetic size effect law (SEL), which has been extensively verified experimentally and theoretically (and is adopted for the 2019 ACI Code, Standard 318, for both beam shear and punching). However, the CSCT derivation and calculation procedure obfuscates the mechanics of failure. It is shown to rest on six scientifically untenable hypotheses, which would have to be taught to students as an article of faith. They make CSCT untrustworthy outside the testing range; ditto for beams with T, I and box cross section, or for continuous beams. The present conclusions are supported by experimentally calibrated finite element simulations of crack path and width, of stress distributions and localizations during failure, and of strain energy release. The simulations also show the CSCT to be incompatible with the “strut‐and‐tie” model, which is (for 2019 ACI Code) modernized to include the size effect in the compression strut. Finally, further deficiencies are pointed out for the Modified Compression Field Theory (MCFT), currently embedded in the Model Code.

Influence of geochemistry on toughening behavior of organic-rich shale

Our research objective is to understand the influence of geochemistry on the fracture behavior of organic-rich shale at multiple length-scales. Despite an increasing focus on the fracture behavior of organic-rich shale, the relationships between geochemistry and fracture behavior remain unclear and there is a scarcity of experimental data available. To this end, we carry out 59 mesoscale scratch-based fracture tests on 14 specimens extracted from 7 major gas shale plays both in the United States and in France. Post-scratch testing imaging reveal fractures with small crack width of about 400 nm. The fracture toughness is evaluated using the energetic size effect law, which is extended to generic axisymmetric probes. A nonlinear anisotropic and multiscale fracture behavior is observed. In addition, a positive correlation is found between the fracture toughness and the presence of of kerogen, clay and calcite. Moreover, the geochemistry is found to influence the timescale and the regime of propagation of the hydraulic fracture at the macroscopic length-scale. In particular, shale systems rich in TOC, clay and calcite are more likely to exhibit high values of the fluid lag and low hydraulic crack width. Our findings highlight the need for advanced constitutive models for organic-rich shale systems and advanced hydraulic fracturing solutions that can fully integrate the complex fracture response of organic-rich shale materials.

Microscopic assessment of bone toughness using scratch tests

Bone is a composite material with five distinct structural levels: collagen molecules, mineralized collagen fibrils, lamellae, osteon and whole bone. However, most fracture testing methods have been limited to the macroscopic scale and there is a need for advanced characterization methods to assess toughness at the osteon level and below. The goal of this investigation is to present a novel framework to measure the fracture properties of bone at the microscopic scale using scratch testing. A rigorous experimental protocol is articulated and applied to examine cortical bone specimens from porcine femurs. The observed fracture behavior is very complex: we observe a strong anisotropy of the response with toughening mechanisms and a competition between plastic flow and brittle fracture. The challenge consists then in applying nonlinear fracture mechanics methods such as the J-integral or the energetic Size Effect Law to quantify the fracture toughness in a rigorous fashion. Our result suggests that mixed-mode fracture is instrumental in determining the fracture resistance. There is also a pronounced coupling between fracture and elasticity. Our methodology opens the door to fracture assessment at multiple structural levels, microscopic and potentially nanometer length scale, due to the scalability of scratch tests.

Size-Effect Law for Scratch Tests of Axisymmetric Shape

AbstractThis paper presents a theoretical and experimental framework for the application of size-effect analysis to microscratch testing as a means to quantify the fracture properties and internal friction of materials at the microscale. The energetic size-effect law (SEL) for microscratch tests is developed for a general monomeric probe shape in terms of an intrinsic size function. The fundamental idea of the proposed approach is to rescale the scratch response to that of the flat punch, a conjecture that allows one to compare the SEL for different probe geometries, and thus solve for the asymptotic fracture toughness and effective process zone length from scratch tests done on homogenous (acetal homopolymer resin and polycarbonate resin) and inhomogeneous materials (mica ceramic and gas shale). As a material of current interest for controlled fracture studies, two samples of gas shale cored from the Marcellus and Eagle Ford formations are tested and analyzed to quantify all material properties that may ...

Energetic Size Effect Law at the Microscopic Scale: Application to Progressive-Load Scratch Testing

AbstractA scratch test consists in pulling a diamond stylus across the surface of a weaker material; it is widely applied in several fields of science and engineering, including polymer damage, metal wear, thin-film quality control, and strength of rocks. Recently, there has been an upsurge of interest in the fracture analysis of materials via scratch testing. In this study, the energetic size effect law (SEL) is applied at the microscopic scale for progressive-load scratch tests using a Rockwell C diamond probe. First, we employ dimensional analysis to connect the scratch force to the projected load-bearing area and to the perimeter for an axisymmetric scratch probe. In a second step, based on geometrical considerations, we approximate the real scratch probe geometry with a cone of equivalent half-apex angle, θeq. Then, we express the dependence of the nominal strength, σN, on the structural size, Λ, via a scaling relationship. The theoretical developments are later implemented in an experimental procedu...

Discussion: Strength-to-fracture scaling in scratching

In their paper, Lin and Zhou (2013) add a new dimension to the scratch test analysis, challenging the applicability of Linear Elastic Fracture Mechanics to scratch tests. The question raised is how to integrate the three-dimensionality of scratch tests into the energetic Size Effect Law (SEL) formulated by Bažant for quasi-brittle materials. We show that Lin and Zhou’s analysis, although relevant is incomplete, as it neglects the blade width, which is critical for the fracture property assessment. In return, if the blade width is properly taken into account, the SEL here proposed is a formidable means to ascertain the fracture toughness from scratching.

Size effect in quasibrittle fracture: derivation of the energetic Size Effect Law from equivalent LEFM and asymptotic analysis

Within the framework of Bažant’s theory, the size effect on the ultimate fracture properties of notched structures is studied from an energy based asymptotic analysis in which the resistance curve behavior is considered through an analytic expression. The scaling on the relative crack length at peak load as well as the size effect on the corresponding resistance to crack growth are investigated. It is shown that, for intermediate structure sizes, the relative crack length at peak load decreases with respect to the structure size while the resistance grows. These scalings lead to a size effect on nominal strength which is in agreement with Bažant’s Size Effect Law (SEL) for small and large structures sizes, but for intermediate sizes, an additional asymptotic regime occurs instead of a simple crossover regime as expected in SEL. The slope and the extent in size of the additional asymptotic regime depend only on the exponent characterizing the curvature of the R-curve. The comparison between the resulting size effect and Bažant’s SEL shows that SEL provides an approximate size effect which is in agreement with the expected asymptotic behaviors, with the exception of the extreme cases corresponding to very strong and slight R-curve’s curvatures. On this basis, the safety design of large structures is discussed.

Size Effect on Compressive Strength of Sandwich Panels with Fracture of Woven Laminate Facesheet

Prismatic sandwich specimens of various sizes, geometrically scaled in the ratio 1:2:4:8, are subjected to eccentric axial compression and tested to failure. The sandwich core consists of a closed-cell polyvinyl chloride foam, and the facesheets are woven glass-epoxy laminates, scaled by increasing the number of plies. The test results reveal a size effect on the mean nominal strength, which is strong enough to require consideration in design. The size effect observed is fitted with the size effect law of the energetic (deterministic) size effect theory. However, because of inevitable scatter and limited testing range, the precise form of the energetic size effect law to describe the test results is not unambiguous. The Weibull-type statistical size effect on the mean strength is ruled out because the specimens had small notches which caused the failure to occur in only one place in the specimen, and also because the observed failure mode was kink band propagation, previously shown to cause energetic size effect. Various fallacies in previous applications of Weibull theory to composites are also pointed out.

Size effect law and fracture mechanics of the triggering of dry snow slab avalanches

A size effect law for fracture triggering in dry snow slabs of high enough length‐to‐thickness ratio is formulated, based on simplified one‐dimensional analysis by equivalent linear elastic fracture mechanics. Viscoelastic effects during fracture are neglected. The derived law, which is analogous to Bažant's energetic size effect law developed for concrete and later for sea ice, fiber composites, rocks, and ceramics, is shown to agree with two‐dimensional finite element analysis of mode II cohesive crack model with a finite residual shear stress. Fitting the proposed size effect law to fracture data for various slab thicknesses permits identifying the material fracture parameters. The value of preexisting shear stress in a thin weak zone of finite length is shown to have significant effect. There exists a certain critical snow depth, depending on the preexisting stress value, below which the size effect disappears. Practical applications require considering that the material properties (particularly the mode II fracture toughness or fracture energy) at the snow slab base are not constant but depend strongly on the slab thickness. This means that one must distinguish the material size effect from the structural size effect, and the combined size effect law must be obtained by introducing into the structural size effect law dependence of its parameters on snow thickness. The thickness dependence of these parameters can be obtained by matching the combined law to avalanche observations. Matching Perla's field data on 116 avalanches suggests that the mode II fracture toughness is approximately proportional to 1.8 power of snow thickness.