Estimated Fracture Toughness Values Research Articles

Fracture-toughness estimation from small-punch test in hydrogen exhibiting ductile and ductile–brittle fracture modes

In this study, an energy-based fracture toughness estimation method based on a small-punch test in a hydrogen environment, exhibiting either ductile or combined ductile and brittle fracture modes is proposed. For the ductile fracture mode, the energy term due to gas pressure in the small-punch test in hydrogen environment is simply added to the existing energy-based fracture toughness estimation equation. For the combined ductile and fracture mode, modified equations for the plastic energy term are proposed to correct overestimation due to brittle cracking. The estimated fracture toughness values are shown to consistent with the published API X70 and X42 test data.

Fracture toughness of single grains and polycrystalline Li7La3Zr2O12 electrolyte material based on a pillar splitting method

In the present study an advanced pillar splitting method is used to determine the fracture toughness of a garnet-type Li7La3Zr2O12 (LLZO) electrolyte. The obtained results are compared to data derived on the basis of conventional Vickers indentation. Furthermore, potential micro-pillar size effects are investigated. The estimated fracture toughness values for single grains and polycrystalline LLZO material obtained via both methods are in good agreement, yielding ∼ 1 MPa m0.5, hence the data indicate that LLZO exhibits relatively low fracture toughness and has a brittle behavior.

On the fracture toughness of bulk metallic glasses under Berkovich nanoindentation

Measurements of fracture toughness from the crack tip opening displacement (CTOD) testing methods are complex and paramount important for a range of bulk metallic glasses (BMGs). In this work, we attempted to propose an indentation protocol to evaluate indentation fracture toughness based on two key considerations: First, the plastic deformation induced damage to the characteristic fracture initiation point calculated from integrating the indentation load-displacement curves is obtained and used to estimate indentation fracture toughness. Second, the continuum damage mechanics theory has been adopted to identify the characteristic fracture initiation point. To verify the applicability of the suggested approach, fracture toughness values of BMGs were estimated and compared with those from CTOD tests in the literature. The estimated fracture toughness values KC obtained from the indentation tests agreed well with those KQ from the CTOD tests within an approximately relative difference of 10%. We also found that KQ linearly correlates with KC (KQ=1.1KC−3.7). The value of KQ in Al-based BMG is predicted to be ~35MPa√m.

Determination of high temperature mechanical properties of thermal barrier coatings by nanoindentation

A nanoindentation method is employed to measure the high temperature mechanical properties, including hardness H, Young’s modulus E and fracture toughness Kc, of 8YSZ (ZrO2+8 wt-%Y2O3) thermal barrier coatings (TBCs) under as sprayed condition and after subjecting them to thermal oxidation. The tests are conducted on the surfaces of YSZ coatings at temperatures of 250 and 450°C. The expressions for indentation H and E are deduced analytically, and the influence of testing temperature and thermal oxidation on them is discussed. An expression for estimating the fracture toughness of the coatings is also derived. The estimated fracture toughness values for the as sprayed YSZ coatings in terms of stress intensity factor at 250 and 450°C are determined to be 1·58 and 0·84 MPa m1/2 respectively. For the oxidised YSZ coatings, these values are 1·35 and 1·10 MPa m1/2 respectively. This study proves that nanoindentation tests can be performed at elevated temperatures for YSZ based TBCs.

Mechanical behavior and failure mechanisms of boron carbide based three-layered laminates with weak interfaces

The effect of weak interfaces on failure mechanisms of a three-layered composite was studied. Three-layered B 4C/B 4C–C nanofibers laminates have been produced using a hot pressing technique. The laminates were designed with thick (∼2.6 mm) outer layers of B 4C and a thin (∼90 μm) center layer of B 4C–70 wt.% C nanofibers. Based on the difference in coefficients of thermal expansion and Young's moduli of the pure B 4C and B 4C–70 wt.% C nanofibers layers, it was estimated that low tensile thermal residual stress with a magnitude of 11.3 ± 2.5 MPa was developed in the thick B 4C outer layers, and compressive residual stress with a magnitude of 455.7 ± 5 MPa was developed in the thin central B 4C–70 wt.% C nanofibers layer. The apparent fracture toughness of laminates was measured and based on the estimated fracture toughness values, a threshold stress was calculated.

Effect of microstructure and strength on the fracture behavior of AA2219 alloy

The plane strain fracture toughness, K J I c and crack growth toughness in terms of the non-dimensional tearing modulus, T R of Al–Cu alloy were evaluated following the J-integral method. An empirical relation is proposed for estimating the fracture toughness from the tensile properties. The estimated fracture toughness values from the empirical relation are found to be in good agreement with the measured fracture data. The microstructural as well as strength variations in the subject alloy were examined through different aging treatments (viz., under aging (UA), natural aging (NA), peak aging (PA) and over aging (OA)). The microstructural observations in different aging conditions were made through transmission electron microscopy (TEM) to understand the type of phase or intermediate stages of the phase present (GP zones, θ″, θ′ or θ). Fracture toughness testing has been carried out on 14 mm thick compact tension (CT) specimens and estimated the crack extension by unloading compliance technique. It was noted that the yield strength increases and fracture toughness decreases with the increase in the degree of aging from NA to PA condition. On overaging the alloy to a yield strength level as that of UA, it was not possible to retain the UA level of fracture toughness. The highest crack growth toughness is exhibited by the NA temper. The fractography analysis revealed that the fracture mode was predominantly transgranular dimpled rupture. Fracture initiation occurred by void nucleation at the second phase particles. The differences in the fracture toughness of the alloy in different aging conditions were shown to be dependent on the differences in the matrix deformation behavior and the strength differential.

Nondestructive Estimation of Fracture Toughness Using Instrumented Indentation Technique

This study focused on the determination of fracture toughness by instrumented indentation technique. A theoretical model to estimate the fracture toughness of ductile materials is proposed and used to verify those results. Modeling of IIT to evaluate fracture toughness is based on two main ideas; the energy input up to characteristic fracture initiation point during indentation was correlated with material’s resistance to crack initiation and growth, and this characteristic fracture initiation point was determined by concepts of continuum damage mechanics. The estimated fracture toughness values obtained from the indentation technique showed good agreement with those from conventional fracture toughness tests based on CTOD. In addition, we confirmed that the proposed model can be also applied in the brittle material through modification of void volume fraction.

Estimation of fracture toughness using miniature chevron‐notched specimens

ABSTRACTAn approach for determining fracture toughness of materials using miniature chevron‐notched specimens is reported here for the first time. An outline of the principle and the experimental procedure for the test is depicted using results generated on eutectoid steel. Fracture toughness values of soft annealed and fully annealed eutectoid steels with inter‐lamellar spacing 167 nm and 549 nm are found to be 76 and 56 , respectively. The estimated fracture toughness values from miniature specimens are found to be in good agreement with the ones reported for similar bulk materials.

EXPERIMENTAL OBSERVATIONS OF THE FAILURE MECHANISMS IN A BULK METALLIC GLASS COMPOSITE

AbstractThe deformation and damage evolution behavior of a Ni-based bulk metallic glass composite reinforced with elongated brass phase is studied under cylindrical indentation. The estimated fracture toughness values based on the energy dissipation and the in-situ observation during the loading reveal the details of the damage evolution and toughening mechanisms in this composite system. The results indicate that the enhanced toughness of the BMG composite is plausibly an outcome of crack bridging mechanisms by the ductile brass phase, rather than a diffused array of nucleated shear bands in the hard BMG and arrest by the ductile reinforcing phase.

An instrumented indentation technique for estimating fracture toughness of ductile materials: A critical indentation energy model based on continuum damage mechanics

We suggest a new instrumented indentation technique for estimating fracture toughness of ductile materials. This technique is based on two key concepts. First, the indentation energy to the characteristic fracture initiation point during indentation may be closely related to a material’s resistance to fracture, i.e., fracture toughness. Second, the characteristic fracture initiation point can be determined by exploiting the basic concepts of continuum damage mechanics. To verify the applicability of the suggested technique, indentation tests and conventional fracture toughness tests were performed on four ductile materials. The estimated fracture toughness values obtained from the indentation technique showed good agreement (within approximately 10% error) with those from conventional fracture toughness tests.

Identifying failure mechanisms of composite structures under compressive load

Various failure mechanisms involving both local and global deformation mechanisms of layered structures, consisting of differently oriented orthotropic laminae, are investigated with a large deformation finite element analysis. Under large compressive loads, fiber-reinforced composite structures can fail by buckling, kink band formation and/or delamination growth. Our aim is to identify the dominant mode which leads to the structural failure under a given boundary condition and geometrical shape. It is assumed that these structures contain initial interlaminar flaws represented by embedded delaminations. Such flaws can play a significant role in defining overall structural integrity and deformation mechanisms. Our study considers two structures with distinguished shapes, both consisting of four layer laminae. The first structure is a flat panel under compressive load and the second structure is a cylindrical shell subjected to external pressure. In both cases, the energy release rate and mixed-mode stress intensity factors are computed to quantify the crack driving force and used to measure likelihood of delamination growth. In the flat panel model, two buckling modes, a global and a local, are observed under quasi-static loading conditions. Depending upon the delamination length and laminate stacking orientations, the interaction of these two modes can produce an unstable post-buckling behavior. It is found that the energy release rate exceeds experimentally estimated fracture toughness values only after buckling occurs. In the cylindrical shell study, lower critical buckling loads are observed for models with longer interlaminar delamination as in the flat panel model. However, unlike the flat panel case, the energy release rate surpasses the critical toughness well before the applied pressure reaches the buckling load of the flawed cylindrical shell. This behavior implies that a shell containing an embedded defect along an interface can fail by delamination growth and therefore has a failure load lower than its critical buckling load. Also, for thicker cylindrical shells, the compressive internal stress exceeds the predicted stress required for kink band formation prior to structural buckling. The competition among these failure modes, buckling, delamination growth and compressive kinking in fiber-reinforced composite structures, is studied and a design diagram is introduced here. This diagram predicts a likely dominant failure mode for given structural dimensions and material properties. In addition, unstable delamination growth along the lamina interface under dynamic loading conditions is simulated using an iterative computational procedure. The results predict that the crack tip velocity can reach a fraction of the material wave speed leading to total structural failure in a very short time. For the cylindrical shell, the inertial effect on the pressure-deformation relation is investigated by comparing it with the static results.