Pre-crack Length Research Articles

Fracture toughness of silicon nitride thin films of different thicknesses as measured by bulge tests

A bulge test setup was used to determine the fracture toughness of amorphous low-pressure chemical vapor deposited (LPCVD) silicon nitride films with various thicknesses in the range 40–108nm. A crack-like slit was milled in the center of each free-standing film with a focused ion beam, and the membrane was deformed in the bulge test until failure occurred. The fracture toughness KIC was calculated from the pre-crack length and the stress at failure. It is shown that the membrane is in a transition state between pure plane-stress and plane-strain which, however, had a negligible influence on the measurement of the fracture toughness, because of the high brittleness of silicon nitride and its low Young’s modulus over yield strength ratio. The fracture toughness KIC was found to be constant at 6.3±0.4MPam1/2 over the whole thickness range studied, which compares well with bulk values. This means that the fracture toughness, like the Young’s modulus, is a size-independent quantity for LPCVD silicon nitride. This presumably holds true for all amorphous brittle ceramic materials.

Mechanism analysis of thermal shock properties for ZrB 2-20%SiCp-10%AlN ultra-high temperature ceramic with the surface defects

An indentation–quenching test was used to characterize thermal shock properties of ZrB 2-20%SiCp-10%AlN ceramic with surface defects that arisen from Vickers indentation. It showed that the thermal shock resistance was affected by the length of pre-crack and the thickness of specimen. The critical temperature difference was up to 550 °C and the residual strength approached to a constant in this paper. Thermal stress intensity factor ( K I) was investigated at temperature of 550 °C by the semi-elliptical surface crack physical model, and it indicated that K I ascended firstly and descended afterwards. The crack propagation behavior was characterized by calculating the difference between the crack resistance and K I. The main influencing factors for K I were also discussed and analyzed here.

On the fracture toughness evaluation in weldments of a maraging steel rocket motor case

Fracture toughness of the weld joints of the maraging steel rocket motor case obtained from the limited Compact Tension (CT) specimens are found to be invalid due to the measured crack lengths through the thickness of the specimens exceeding 10% of the initial crack length. This paper proposes an indirect method to evaluate the pre-crack length of the CT specimen from the recorded load versus crack mouth opening displacement data. The Chauvenet’s criterion is applied. After confirming the initial crack size and other validity conditions, the evaluated fracture toughness is designated as the plane-strain fracture toughness ( K IC ).

Back‐Face Strain for Monitoring Stable Crack Extension in Precracked Flexure Specimens

Calibrations relating back‐face strain (BFS) to crack length in precracked flexure specimens were developed for different strain gage sizes. The functions were verified via experimental compliance measurements of notched and precracked ceramic beams. Good agreement between the functions and experiments occurred, and fracture toughness was calculated using several operational methods: maximum test load and optically measured precrack length; load at 2% crack extension and optical precrack length; and maximum load and BFS crack length. All the methods gave comparable results. The initiation toughness, KIi, was also estimated from the initial compliance and load. The results demonstrate that the stability of precracked ceramic specimens tested in four‐point flexure is a common occurrence, and that methods such as remotely monitored load‐point displacement are only adequate for detecting stable extension of relatively deep cracks.

A Three-Dimensional Finite Element Analysis of the Stress Intensity Factors for Different Fracture Modes of Homogeneous Bimaterial

Abstract The failure of cracked components is governed by the stresses in the vicinity of the crack tip. The singular stress contribution is characterized by stress intensity factors. The stress intensity factors depend on the geometry of the component and on loading condition. This paper addresses the evaluation of stress intensity factors (SIFs) of opening, shearing and tearing modes for compact tension specimens for bonding homogeneous materials. The aim of this work is to find the optimal pre-cracked length, crack notch radius, and crack notch angle in order to eliminate the effect of them on the SIF and then on the fracture toughness. To achieve this goal, a three- dimension finite element analysis (FEA) model using the ANSYS program is constructed for specimens made of homogeneous materials such as stainless steel bonding with epoxy as a filler material. The effects of notch angle, notch tip radius and pre-crack length on the stress intensity factors are studied for different fracture modes. The results for the stress intensity factors KI, KII and KIII are obtained using the linear elastic fracture mechanics (LEFM) approach.

Experimental characterization of the crack-tip-opening angle in fibre metal laminates

Although the crack-tip-opening angle (CTOA) has been shown to be well suited for modelling stable crack growth in monolithic sheet aluminium alloys, its applicability for fibre metal laminates has not been fully analyzed yet. Fracture test were performed on M(T) panels made of Glare 2-3/2-0.4, Glare 3-3/2-0.4 and laminated 2024-T3 3/2-0.4. Different fatigue pre-crack lengths were created to study the effect of bridging fibres on the CTOA measured on the external layer. The effect of bridging fibres resulted in small deviations of the CTOA vs. crack extension curve with respect to the reference panel made of metal laminate. The CTOA criterion could be successfully used for predicting the residual strength in fibre metal laminates.

21317 エポキシ系接着剤による異材継手の3点曲げ破壊試験(材料強度と実験力学(4),OS.3 材料強度と実験力学,学術講演)

The objective of this study is to investigate the strength of epoxy adhesively bonded dissimilar materials at different bond thickness with interfacial pre-crack. From three-point bending (3PB) fracture test of adhesive joints, it is observed that the fracture strength decreases as the bond thickness increases. Nevertheless, fracture strength of 3PB adhesive joints with interfacial pre-crack is independent on bond thickness. The interfacial crack-tip inside the adhesive joints of dissimilar material has also experienced Mode II manner when it is subjected to Mode I loading. In addition, for 3PB adhesive joints with aluminium/adhesive interfacial crack, it is found that Jc is dependent on pre-crack length, thus there is a change in fracture behavior. Moreover, such behavior is also observed from numerical analysis.

Evaluation of Precracking Methods for the End-Notched Flexure Test

*† Results are presented from a study to evaluate and develop static mode II precracking methods for use with the end-notched flexure test. Precracking followed by fracture toughness testing was performed on specimens from two different materials. Precracking was performed using both the four-point bend and conventional three-point bend endnotched flexure geometries. All testing was performed in the latter geometry. There was no difference in the precracks created by the two geometries. However, delamination toughness was observed to strongly depend on the amount of dynamic crack advance that occurs during the precracking process. This was hypothesized to be due to the faster crack speeds that are associated with larger amounts of advance. To address this, various precracking geometries were evaluated in order to determine those that would produce precracks that were essentially straight, perpendicular to the direction of crack advance, and of sufficient length to produce a precracked toughness at or near the minimum value that occurs with increasing precrack length. This results in a recommended geometry for use with the endnotched flexure test that is appropriate for both precracking and testing, and which therefore allows for non-precracked and precracked toughnesses to be obtained from the same test specimen.

Micromechanical Analysis of Constraint Effect on Fracture Initiation in Strength Mismatched Welded Joints

In this paper the micromechanical approach to ductile fracture was applied in a study of constraint effect on crack growth initiation in mismatched welded joints. The single-edged notched bend specimens (precrack length a0/W=0.32) were experimentally and numerically analyzed. The coupled micromechanical model proposed by Gurson, Tvergaard and Needleman was used. Constraint effect was tested by varying widths of the welded joints (6, 12 and 18mm). Highstrength low-alloyed (HSLA) steel was used as the base metal in a quenched and tempered condition. The flux-cored arc-welding process in shielding gas was used. Two different fillers were selected to obtain over- and undermatched weld metal. The micromechanical parameters used in prediction of the crack growth initiation on precracked specimen were calibrated on a round smooth specimen. The difference in fracture behavior between over- and undermatched welded joints obtained in experimental results was followed by numerical computations of void volume fraction in front of the crack tip.

Numerical Analysis on Surface Fractures in Two-Layered Materials Subjected to Thermal Loading

With the knowledge of heterogeneous characteristics of thermal barrier coating materials at mesoscopic level, a coupled thermo-mechanical-damage (TMD Model) model was introduced and used to numerically quantify the thermal stresses and crack development of in thermal barrier coatings (TBCs) composite subjected to decreased temperatures. The effect of different surface precrack morphologies, such as precrack length and precrack density, on an interface crack subjected to thermal loading caused by a temperature change is presented. It provides us with a more sensible physical intuition and a more accurate mathematical for optimizing the design and the processing of ceramic coatings subjected to the coupled thermal-mechanical loading.

Fracture behavior of the compact tension specimens in NiTi shape memory alloys

In the present work, the fracture behavior of a NiTi pseudoelastic alloy has been investigated. The fracture toughness is obtained by experiments on compact tension (CT) specimens, which are pre-cracked at a low fatigue load. The fracture toughness of the studied material is K IC = 39.4 MPa m 1/2. The fracture surface of selected specimen is studied by scanning electron microscope (SEM). It is found that the fracture mechanism is dominated by cleavage fracture. With the increasing crack velocity, the fracture surface at the fast fracture regime exhibits a more brittle response. The finite element simulation on both specimens with and without pre-crack is carried out to better understand the fracture mechanisms of the NiTi alloys. It is shown that a pre-crack results in phase transformation at the crack tip under very low load. However, due to the low fatigue load and short pre-crack length, the material is always partly phase transformed, even at the crack tip, during the fatigue pre-crack process. There is always a small area around the crack tip fully transformed during the fast fracture process.

Measuring the fracture toughness of ultra-thin films with application to AlTa coatings

An experimental technique is presented for measuring the fracture toughness of brittle thin films. In this technique, long rectangular membranes are fabricated from the film of interest using standard silicon micromachining techniques. A focused ion beam is then used to introduce pre-cracks of different lengths along the centerline of the membranes and the membranes are pressurized until rupture. The fracture stress of the membrane is measured as a function of pre-crack length and the fracture toughness of the film is determined from a simple fracture mechanics analysis. The technique is applicable to a wide range of materials and is especially suited for ultra-thin films. We have demonstrated the experimental procedure for a 150 nm AlTa intermetallic film and obtained a room-temperature fracture toughness of K 1c = 4.44 ± 0.21 MPam1/2.

Modelling of ductile fracture initiation in strength mismatched welded joint

In this paper, the effect of strength mismatch and width of the welded joints on the stress–strain distribution in the crack tip region has been discussed. The single-edge notched bend (SENB) specimens (precrack length a 0/ W = 0.32) were experimentally and numerically analysed. The model of local approach to fracture, proposed by Gurson, Tvergaard and Needleman, was used. High-strength low-alloyed (HSLA) steel was used as a base metal in quenched and tempered condition. The flux-cored arc-welding process in shielding gas was used. Two different fillers were selected to make over- and undermatched weld metal. The experimental analysis of fracture behaviour of the over- and undermatched welded joints was followed by numerical computations of void volume fraction in front of the crack tip. The critical void volume fraction, f c, used in prediction of the crack growth initiation on the SENB specimen had been previously determined on a round smooth specimen. Three widths of weld metal were considered: 6, 12 and 18 mm. A comparison of the crack tip opening displacement (CTOD) values corresponding to crack initiation in the SENB specimens is given, as determined both experimentally and using the GTN model.

Three-Dimensional Finite Element Model for Evaluation the Stress Intensity Factors for Different Fracture Modes of Homogeneous Bimaterial

The failure of cracked components is governed by the stresses in the vicinity of the crack tip. The singular stress contribution is characterized by stress intensity factors. The stress intensity factors depend on the geometry of the component and on loading condition. This paper addresses the evaluation of stress intensity factors (SIFs) of opening, shearing and tearing modes for compact tension specimens for bonding homogeneous materials. The aim of this work is to find the optimal pre-cracked length, crack notch radius and crack notch angle in order to eliminate the effect of them on the SIF and then on the Fracture toughness. To achieve this goal, a three-dimension finite element analysis (FEA) model using ANSYS program is constructed for specimens made of homogeneous materials such as stainless steel bonding with epoxy as a filler material. The effects of notch angle, notch tip radius and pre-crack length on the stress intensity factors are studied for different fracture modes. The results for the stress intensity factors KI , KII and KIII are obtained using linear elastic fracture mechanics (LEFM) approach.

Energy considerations in crack deflection phenomenon in single crystal silicon

Crack deflection in single-crystal brittle occurs when a crack, propagating on one cleavage plane, ‘chooses’, from energy considerations, to continue propagating on another cleavage plane. This phenomenon was identified during dynamic crack propagation experiments of thin, rectangular [0 0 1] single-crystal (SC) silicon specimens subjected to three-point bending (3PB). Specimens with long pre-cracks (hence propagating at a ‘low’ energy and velocity) cleave along the vertical (1 1 0) plane, while the same specimens but with short pre-cracks (and therefore with higher propagation energy and velocity) cleave along the inclined (1 1 1) plane. The same specimens with intermediate pre-crack length show that the crack first propagates on the (1 1 0) plane and then deflects to the (1 1 1) plane. We show that the deflection is due to variations of the material property that resists cracking, Γ, the dynamic cleavage energy, with velocity and crystallographic orientation. We propose selection criteria to explain the deflection: The crack will deflect to the plane with the lowest dynamic cleavage energy. We further suggest that crack deflection is the basic mechanism controlling the way the crack consumes energy while propagating and is the main cause of surface perturbations. The spatial temporal fracture energy along the (1 1 0) cleavage plane is evaluated.

R-curve behavior of Ti 3SiC 2

One of the characteristic material properties for many of the high toughness ceramics (ZrO 2, Sialon, etc.) is the enhanced resistance to crack growth during crack extension, a phenomenon known as ‘R-curve behavior’. Herein, we report, the crack growth resistance/R-curve behavior of Ti 3SiC 2. The crack growth resistance property of Ti 3SiC 2 is experimentally measured using single-edge-precrack-notched beam (SEPB) method. At room temperature, the flexural tests of hot pressed Ti 3SiC 2 bars are performed under 4-point bending mode and the precrack length is varied in our experiments. Additionally, the fracture toughness/crack growth resistance behavior as well as fracture mechanisms of Ti 3SiC 2 are explained on the basis of microstructure and bonding in Ti 3SiC 2. SEM investigation reveals significant crack wake bridging, which is a characteristic feature of many high toughness damage-tolerant ceramic.

Effect of crack configuration and pre-crack length on stress intensity factors

Abstract In this paper, the results for the stress intensity factor of a mode III (tearing mode) have been investigated using the method of finite element analysis. A compact tension specimen containing a pre-crack and subjected to out-of-plane tearing loads has been used. A three-dimensional finite element analysis (FEA) model using the ANSYS program has been built for specimens made of different bio-medical materials such as stainless steel, titanium, alumina, high density polyethylene(HDPE) and polymethyl methacrylate(PMMA). Such materials are used for hip and knee replacement and for dental implants. The effects of notch angle, notch tip radius and pre-crack length on the stress intensity factor for the mode III have been studied. The model was extended to study the effect of crack and bonding line separation distance on stress intensity factors for specimens made of different homogeneous materials such as stainless steel bonding with epoxy as a filler material. The number of elements along the crack front and crack tip has been varied to determine its effects on the stress intensity factors. It is concluded that the pre-crack must be greater than or equal to 33% of the total crack lengt and the notch must be a blunt notch in order to obtain the stress intensity factor, KII I, independently, of the crack notch angle. However, the stress intensity factor is independent of the crack and bonding line separation distance when it is less than or equal to 15% of the specimen width. The results for the stress intensity factors, KII I, are obtained using a linear elastic fracture mechanics (LEFM) approach.

Effect of notch configuration and pre-crack length on stress intensity factors

Abstract The determination of stress intensity factors for specimens with pre-cracks is important in fracture analysis. In this paper, the evaluation of stress intensity factors of modes I and II for compact tension specimens is presented. A 3-D finite element analysis (FEA) model using the ANSYS program is constructed for specimens made of different bio-medical materials such as stainless steel, titanium, alumina, high density polyethylene (HDPE) and polymethyl methacrylate (PMMA). Such materials are used for hip and knee replacement and for dental implants. The effects of notch angle, notch tip radius and pre-crack length on the stress intensity factor are studied. The number of elements along the crack front and crack tip is considered and has been varied to determine its effect on the value of the stress intensity factor. It is concluded that, in order to evaluate the reasonable values for the stress intensity factor, the pre-crack lengt should be greater than 10% and 33% of the total crack lengt for modes I and II, respectively. The results for the stress intensity factors KI and KII are obtained using a linear elastic fracture mechanics (LEFM) approach.

Determination of interface fracture toughness of adhesive joint subjected to mixed-mode loading using finite element method

In this study, a compact mixed-mode (CMM) specimen, which comprises an adhesive joint and a loading fixture, is employed to determine interface fracture toughness of an adhesively sandwiched joint with an interface edge crack subjected to global mixed-mode loading. An interface mechanics-based finite element (FE) method is developed to simulate the stress and displacement distributions around the tip of an interface edge crack situated in the sandwiched joint. A small region crack-tip opening displacement (CTOD)-based linear extrapolation method is developed to determine stress intensity factors (SIFs) at the crack-tip. Effect of pre-crack length on the SIFs is studied and a length range of pre-crack is proposed for the determination of SIFs. Furthermore, these methodologies are applied to characterize the critical interface fracture toughness of the sandwiched joint. Three types of fracture criteria, i.e., modes I and II critical fracture toughness-based failure assessment diagram (FAD), effective critical fracture toughness-based failure assessment criterion (FAC), and strain energy release rate-based FAC, are established for the reliability design and failure assessment of the adhesively bonded sandwich joint.

The Effect of Negative Stress Ratio Load History on High Cycle Fatigue Threshold

Abstract The objective of this research was to measure the load history effects of negative stress ratio loading on the high cycle fatigue (HCF) crack growth threshold of Ti-6Al-4V. Previous work has shown an increase in the HCF threshold that is dependent on the Kmax during the low cycle fatigue loading that nucleated a crack. The increase in fatigue limit was attributed to an overload effect from the LCF loading and was quantified through the use of a simple overload model. On the contrary, evidence from R = −1 testing suggests that negative overloads, referred to as underloads, may reduce this Kmax load history effect and even lower the threshold below long crack values. To investigate this further, smooth and notched Ti-6Al-4V specimens were pre-loaded in fatigue below their endurance limit at stresses expected to nucleate cracks in approximately 10 million and 100 000 cycles, respectively, and at stress ratios of −3.5 and −3, respectively. Although the smooth specimens could not be monitored for crack nucleation, the notched specimens allowed the use of an infrared damage detection system to monitor the localized region at the notch root for indications of crack nucleation. These cracked specimens were then heat tinted, and several were also stress relieved to remove load history effects. All of the preloaded specimens were then HCF step tested to determine the fatigue limit stress or threshold. Although the smooth bars showed little effect due to the preloading at negative R, the threshold results on the notched specimens that developed measurable cracks seem to show competing effects of underloading and Kmax overloading, dependent somewhat on precrack length. The specimens with smaller cracks nucleated at R = −3 tend to have a reduced HCF threshold compared to the conventional long crack threshold. Short crack effects and load-history effects are quantitatively explained with the aid of a Kitagawa diagram with an El Haddad short crack correction.