Four-point Bend Specimens Research Articles

On the mechanism and the length scales involved in the ductile fracture of a bulk metallic glass

Some bulk metallic glasses (BMGs) exhibit high crack initiation toughness due to shear band mediated plastic flow at the crack tip and yet do not display additional resistance to crack growth due to the lack of a microstructure. Thus, at crack initiation, the fracture behavior of BMGs transits from that of ductile alloys to that of brittle ceramics. In this paper, we attempt to understand the physics behind the characteristic length from the notch root at which this transition occurs, through testing of four-point bend specimens made of a nominally ductile Zr-based BMG in three different structural states. In the as-cast state, both symmetric (mode I) and asymmetric (mixed mode) bend specimens are tested. The process of shear band mediated plastic flow followed by crack initiation at the notch root was monitored through in situ imaging. Results show that stable crack growth occurs inside a dominant shear band through a distance of ∼60μm, irrespective of the structural state and mode mixity, before attaining criticality. Detailed finite element simulations show that this length corresponds to the distance from the notch root over which a positive hydrostatic stress gradient prevails. The mean ridge heights on fractured surfaces are found to correlate with the toughness of the BMG. The Argon and Salama model, which is based on the meniscus instability phenomenon at the notch root, is modified to explain the experimentally observed physics of fracture in ductile BMGs.

Initiation of ductile fracture in mixed-mode I and II aluminum alloy specimens

This study investigates the initiation of mixed-mode crack extensions in four-point bend and shear specimens fabricated from aluminum alloys. The determination of fracture initiation utilizes a new strain detection method, which provides a uniform criterion for specimens over the complete mixed-mode I–II loading range. The 0.2mm offset method for mode I specimens and the physical features on the fracture surface of mode II dominant specimens validate this method. The total measured fracture toughness shows a minimum value for the pure mode I case, a maximum for the pure mode II case and an oscillated trend over the mixed-mode I–II loads.

Computation of V-notch shape factors in four-point bend specimen for fracture tests on brittle materials

Four-point bend (FPB) specimen is an important test sample in mixed mode fracture study of notched components made from brittle materials like rocks, brittle polymers, ceramics, etc. On the other hand, the notch stress intensity factors (NSIFs) are vital parameters in brittle fracture assessment of V-notched structures. Therefore, computation of NSIFs in FPB specimens is of practical interest to engineers and researchers. Since the available methods for calculating the NSIFs are often cumbersome and need complicated calculations, it is preferred to show them as a set of dimensionless parameters for the FPB specimen. In this research, the finite element method coupled with a recently developed algorithm called FEOD is employed to calculate the NSIFs of a FPB specimen for several V-shape notches and for different combinations of mode I and mode II. The obtained NSIFs are then converted to dimensionless parameters called notch shape factors and are illustrated in a number of figures. It is shown that depending on the notch depth and the location of loading points, full mode mixity from pure mode I to pure mode II can be provided in the FPB specimen. The numerical results obtained in this research are verified by using very limited results reported earlier in literature.

A supplementary study on fracture tests of piezoelectric material: cracks parallel to the poling direction

This study focuses on the behavior of a crack in piezoelectric material in which the crack is parallel to the poling direction. Tests were carried out on four-point bend specimens made of PZT-5H (Morgan Electro Ceramics, Wrexham, UK). Cracks were introduced parallel to the poling direction. With an electric field induced perpendicular to the cracks, the load was increased until failure occurred. Using the load at fracture, the level of the electric field and the critical crack length, finite element analyses were carried out to determine the intensity factors. These included K I , K IV and a small K II component. The latter occurred because of the small asymmetry of the crack. The material within the crack (air) was modeled to be a dielectric material. A fracture criterion is implemented in which the test results show small scatter about the failure curve. These tests were carried out in order to improve on the scatter obtained from a previous set of tests presented in Motola et al. (Int J Fract 159:167–190, 2009a). The scatter from those results will be explored.

Evaluation of interfacial toughness curve of bimaterial in submicron scale

A novel method combining the experimental data at only two different mixed mode fractures and an empirical interface toughness function has been proposed to establish the interfacial toughness function of a bimaterial in submicron scale. The modified four-point bend specimen was used in experiment to evaluate the first type of mixed mode fracture, while the sandwiched cantilever specimen was employed to get the second one. An empirical interface toughness function reflecting quite accurately the delamination behavior was adopted as a typical one. The obtained results investigated that the proposed method could be used to calibrate not only the interfacial fracture criteria at pure modes but also at any mixed mode fracture of bimaterials in submicron scale.

Potentials of the “Direct inkjet printing” method for manufacturing 3Y-TZP based dental restorations

Abstract The potentials of the direct inkjet printing (DIP) method for manufacturing 3Y-TZP dental restorations were investigated. Aqueous inks of 3Y-TZP and carbon were developed and characterised for the DIP method. A sample 3Y-TZP framework of a dental bridge was produced by DIP. The stress distribution on this framework under realistic clenching conditions was simulated using finite element analysis. Four-point bending specimens produced by DIP and a slip cast reference sample were tested to characterise the flexural strength of the DIP produced components.

Analysis of miniature single- and double-notch bending specimens for estimating the fracture toughness of cortical bone

Studies of the fracture behavior of cortical bone have determined multiple toughening mechanisms that are active during propagation of a crack. Common methods for measuring bone fracture toughness use single-notched specimens often in four-point (SN4PB) or three-point bending (SN3PB). A double-notch four-point bending (DN4PB) specimen is useful to study prefailure damage at the crack tip. Total failure occurs at one notch and only partial failure at the other allowing study of prefailure damage in the unbroken notch. There is no widely known method for calculating the fracture toughness of bone using a DN4PB specimen. A method for calculating the fracture toughness of cortical bone using a DN4PB is developed here and compared with results for a common SN3PB specimen. The new double-notch method permits using a single specimen to measure apparent fracture toughness and to study both pre- and postfailure microdamage in the bone matrix. When and how to use the new and the established test specimens for understanding bone mechanics is discussed.

Fracture toughness of bonds using interfacial stresses in four-point bending test

Bond strength is an important factor in electronic and photonic packaging. Measuring bond characteristics, strength, and fracture toughness is particularly difficult in microelectronic devices where miniaturized bonds are used (e.g., wafer bonding and 3 dimensional integrated circuits). Since applying load directly to the bonds is proven difficult, four-point bending test with notched specimen has been typically used to facilitate fracture toughness measurements at small scale. This method is based on experiencing large peeling and shear stresses at the interface of two layers of different materials at the notch. However, there is a lack of analytical solution that can be used to determine the peeling and shear stresses at the interface of four-point bend specimen. This manuscript presents analytical modeling of peeling and shear stresses in tri-layer four-point bend specimens. Strength of materials approach with the assumption of small strains, within elastic region, is adopted in this study for evaluation of stresses and displacements. Furthermore, beam theory is utilized to develop equations that describe the moments and shear forces in the assembly due to the four-point bending loads. Second and fourth order differential equations are derived for shear and peeling stresses respectively at the interfaces of the assembly. Boundary conditions are determined based on load, supports and shear force and moment diagrams of the assembly. The problem solution is obtained by solving the governing differential equations instantaneously using standard methods. Finite-Element-based simulation is used to compare with and verify the analytical solution. This work also presents an alternative approach where the stresses at the notch are used to determine the fracture toughness. An experiment is conducted on a specimen with intermetallic material as bond material. The analytical approach is then verified with the results of four-point bending experiment and is validated using the conventional technique (which is based on energy equilibrium and presented by Eq. (60)).

Cohesive zone criterion for cracking along the Cu/Si interface in nanoscale components

Crack initiation and propagation along the Cu/Si interface in multilayered films (Si/Cu/SiN) with different thicknesses of the Cu layer (20 and 200 nm) are experimentally investigated using a nano-cantilever and millimeter-sized four-point bending specimens. To examine the cohesive zone model (CZM) criterion for interfacial delamination along the Cu/Si interface in nanoscale stress concentration, an exponential type of CZM is utilized to simulate the observed delamination processes using the finite element method. After the CZM parameters for the Cu/Si interface are calibrated by experiment, interface cracking in other experiments is predicted. This indicates that the CZM criterion is universally applicable for describing cracking along the interface regardless of specimen dimensions and film thickness which include the differences in plastic behavior and residual stress. The CZM criterion can also predict interfacial cracking along Cu/Si interfaces with different stress singularities.

Sensitivity of stress corrosion cracking of stainless steel to surface machining and grinding procedure

An investigation has been undertaken to establish the effect of surface preparation method on the susceptibility of a 304 stainless steel to stress corrosion cracking under simulated atmospheric corrosion conditions. MgCl 2 was deposited onto four-point bend specimens, which were then placed in a chamber with a relative humidity of 45% and temperature of 60 °C. These test conditions were designed to reflect external exposure of stainless steel components in industrial plant, including nuclear reactor components, situated in a coastal region, but with the severity of the exposure conditions enhanced to allow discrimination of the effect of surface preparation in a short timescale (up to 1500 h). Four surface preparation methods were evaluated: transverse grinding, longitudinal grinding, transverse dressing using an abrasive flap wheel, and transverse milling. For each case, surface topography, surface defect mapping, near-surface microhardness mapping, residual stress and electron back-scattered diffraction measurements were undertaken. Stress corrosion cracks were observed for the ground and milled specimens but not for the dressed specimens, with cracks apparently originating at corrosion pits. The density of cracks increased in the order: transverse ground, milled and longitudinal ground, with the cracks notably much smaller in length for the transverse ground condition. The propensity for cracking could be linked to the high residual stress and apparent nanocrystalline microstructure at the surface. There was a greater propensity for pitting to initiate at local defect sites on the surface (laps, deeper grooves). However, the tendency was not overwhelming, suggesting that other factors such as more general roughness or the distribution of MnS inclusions had an influence, perhaps reflecting the severity of the environment.

Interlamellar cracking of thermal barrier coatings with TGOs by non-standard four-point bending tests

Abstract This work concerns the failure mode and fracture toughness of plasma-sprayed 8 wt% yttria-stabilized zirconia (8YSZ) deposited on a cold-sprayed MCrAlY bond coat (BC) after thermal oxidation. Upon high-temperature exposure, a thermally grown oxide (TGO) layer was formed along the interface between the BC layer and YSZ ceramic coating layer through oxidation of the bond coat. By utilizing a non-standard modified four-point bending specimen, in conjunction with fractured surface examinations by scanning electron microscope and energy disperse spectroscope, the failure mode of this thermal barrier coating (TBC) system has been checked experimentally. It is shown that delamination cracks firstly initiate at the YSZ/BC interface edge, and then propagate along a wavy path near the interface, not only through the TBC but also within the TGO and along the interlamellar interfaces. Through a theoretical analysis of the bending specimen, the fracture toughness of this TBC system, in terms of strain energy release rate, has been determined from the load–displacement curves which were recorded during the tests.

High yield four-point bend thin film adhesion testing techniques

Novel four-point bend specimen geometries are proposed for improved test yield over standard four-point bend specimens when measuring high-strength and ultra-thin film structures. The fracture energies of both a Cu/SiN dielectric diffusion barrier interface and a high-k/metal gate (HfO2/Pt–Ti metal bilayer) interface are reported. Four novel specimen types were evaluated and result in significantly increased test yield as compared to the standard four-point bend specimens. The modified four-point bend specimens were fabricated by altering the crystallographic orientation, width, and thickness of the beams which make up the specimen. The mechanics of the four-point bend test are discussed for each different specimen type. The increased test yield is explained in terms of the stresses which develop in the specimen during testing, the phase angle of loading experienced for each specimen type, and the anisotropic fracture properties of single crystal silicon.

On the use of an anti-symmetric four-point bend specimen for mode II fracture experiments

The edge-cracked beam specimen subjected to anti-symmetric four-point bend (ASFPB) loading has been conventionally used in the past for investigating the pure mode II fracture experiments in many engineering materials. However, it is shown through finite element analysis that the ASFPB specimen sometimes fails to produce pure mode II conditions. For anti-symmetric loads applied close to the crack line, there are considerable effects from KI and T-stress in the ASFPB specimen. Pure mode II is provided only when the applied loads are sufficiently far from the crack plane.

Short fatigue crack growth from a blunt notch in plate specimens

Short crack growth behavior from a notch including crack closure and load ratio effects was investigated. Experiments and analyses were carried out using four-point bending specimens made of SAE 1045 steel, using a blunt notch keyhole specimen geometry. The lower the load ratio, the more notch effect on short crack growth behavior was observed. Short cracks in the notch affected zone had higher growth rates than long cracks. After the crack grew out of the notch effect field, short crack growth rates merged with the long crack growth rates. Several parameters were used to correlate the short crack growth rates including stress intensity factor range, effective stress intensity factor range, and stress intensity factor range based on notch root stress.

Fracture toughness measurements of plasma-sprayed thermal barrier coatings using a modified four-point bending method

Abstract In this study, the adhesion strength of thermal barrier coatings 8YSZ (ZrO2 + 8 wt.% Y2O3) deposited on NiCrAlY bond coats by atmospheric plasma spraying is investigated experimentally. A modified four-point bending specimen that can generate a single interface crack to facilitate the control of crack growth was adopted for testing. The fracture surfaces were examined using a scanning electron microscope. Images show that cracks are initiated along YSZ/NiCrAlY interfaces, then kink and grow uniformly within the YSZ layer. The load–displacement curves obtained indicate three distinct stages in crack initiation and stable crack growth. Based on a microstructural model, finite element analyses were performed to extract the bonding strength of the thermal barrier coatings. The fracture toughness of the plasma-sprayed 8YSZ coatings, in terms of critical strain energy release rate Gc, can be reliably obtained from an analytical solution or from a numerical simulation of the cracking process using compliance methods.

Short fatigue crack growth behavior under mixed-mode loading

Mixed-mode loading represents the true loading condition in many practical situations. In addition, most of the fatigue life of many components is often spent in the short crack growth stage. The study of short crack growth behavior under mixed-mode loading has, therefore, much practical significance. This work investigated short crack growth behavior under mixed-mode loading using a common medium carbon steel. The effects of load mixity, crack closure, and load ratio on short crack growth behavior were evaluated by conducting experiments using four-point bending specimens with several initial KII/KI mixed-mode ratios and two load ratios. Cracks were observed to grow along the paths with very small KII/KI ratios (i.e. mode I). The maximum tangential stress criterion was used to predict the crack growth paths and the predictions were found to be close to the experimental observations. Several parameters including equivalent stress intensity factor range and effective stress intensity factor range were used to correlate short crack growth rates under mixed-mode loading. Threshold values for short cracks were found to be lower than those for long cracks for all the mixed-mode loading conditions. Crack closure was observed for the entire crack length regime with all load mixity conditions at R ≈ 0.05 and for short crack regime under high load mixity condition at R = 0.5. Several models were used to describe mean stress effects and to correlate crack growth rate data.

Determination and analysis of crack growth resistance in plasma-sprayed thermal barrier coatings

Abstract Ceramic thermal barrier coatings (TBCs) are increasingly applied to enhance the performance of advanced gas turbine engines. However, the delamination cracks initiated in these coatings limit their applications. In this research, a sandwiched four-point bend specimen is used to evaluate the crack growth resistance in plasma-sprayed TBCs. Well controlled, stable and measurable crack extension is obtained. A rising crack growth resistance curve is found. The steady state strain energy release rate is obtained to be about 170 J/m 2 . The delamination crack evolution behavior is in situ observed and simulated by the finite element analysis based on a crack bridging model.

Importance of Residual Stresses and Surface Roughness regarding Fatigue of Titanium Forgings

Abstract This paper presents the results of a long-term research program aimed at developing qualitative and quantitative design guidelines for the use of mechanical surface treatments designed to improve the fatigue life of structural components. High cycle fatigue tests were performed on planar four-point bending specimens derived from Ti-6Al-4V pancake forgings with a mill-annealed microstructure. The high cycle fatigue behavior of specimens with different surface conditions (as-forged and machined) in both an unpeened and a shot peened state was compared. In order to assess the fatigue failure mechanisms, detailed investigations of the surface layers were carried out. The as-forged surface state exhibits a stress distribution with significant compressive stresses near the surface, resulting in equilibrium tensile stresses in the depth. When the tensile stresses were exposed by machining a bordering surface, a distinct decrease in the fatigue strength was observed. In such cases, a shot peening treatment was shown to improve the fatigue strength. Square edges lead to a decrease in the fatigue strength, which could be aggravated by shot peening.

Hydrogen effect on fracture toughness of thin film/substrate interfaces

The effect of hydrogen on the interface fracture toughness of two nano-film/substrate structures, Ni/Si and Cu/Si, were evaluated using four-point bend specimens with and without hydrogen charging. Hydrogen typically decreases the fracture toughness of materials. However, we found in this study that the interfacial toughness between the Ni film and the Si substrate increased due to the presence of hydrogen, while that of Cu/Si decreased. Nanoindentation experiments for the Ni and Cu films revealed that local plasticity in the Ni and Cu films is promoted by the charged hydrogen. The critical stress intensity at the Ni/Si interface crack considering the plasticity of Ni, namely the true fracture toughness, is scarcely influenced by the existence of hydrogen. The apparent increase in fracture toughness of the Ni/Si interface is due to the large stress relaxation near the crack tip caused by softening due to the presence of hydrogen. Although the promotion of plastic deformation of Cu relaxes the stress intensity at the Cu/Si interface crack, the apparent interfacial toughness still decreases because of the significant decrease in the true toughness due to the presence of hydrogen.

Effect of thermal mismatch induced residual stresses on grain boundary microcracking of titanium diboride ceramics

The effect of thermal mismatch induced residual stresses on grain boundary microcracking in titanium diboride (TiB2) ceramics has been studied by finite element method. A cohesive zone model was used to simulate the microcracking initiation in four-point bending specimens. In particular, the microcracking was assumed to occur at a grain boundary which is located in the center of the specimen, surrounded by a thermally anisotropic area. The predicted failure strength appears to be significantly reduced by the presence of residual stresses when the cohesive energy of the microstructure is small. The failure load from experiments has been used to determine the critical damage parameters for microcracking initiation in both pristine and aluminum-infiltrated TiB2. A viscous regularization technique is employed in the simulations to improve the rate of convergence of the solution and the effect of the value of the viscosity parameter on the simulation results, has been investigated. The effect of grain size, grain orientation, and number of employed thermally anisotropic grains, on the microcracking is also discussed.