A dynamic analysis of modified compact-tension specimens using homalite-100 and polycarbonate plates

The dynamic fracture and crack-arrest responses of a modified compact-tension specimen (M-CT) machined from Homalite-100 and polycarbonate sheets were studied by dynamic photoelasticity, dynamic finite-element analysis and streaking photography. In contrast to some of the published results involving steel M-CT specimens, substantial dynamic effects were observed during rapid crack propagation in the Homalite-100 and polycarbonate M-CT specimens. The dynamic crack-arrest toughnesses.K _1a , were relatively constant and were about 80 percent and 50 percent of the corresponding fracture toughness,K _1c , of Homalite-100 and polycarbonate, respectively.     

On the relationship between critical tensile stress and fracture toughness in mild steel

An analysis is presented which relates the critical value of tensile stress (σ_f) for unstable cleavage fracture to the fracture toughness (K_Ic) for a high-nitrogen mild steel under plane strain conditions. The correlation is based on (i) the model for cleavage cracking developed by E. Smith and (ii) accurate plastic-elastic solutions for the stress distributions ahead of a sharp crack derived by J. R. Rice and co-workers. Unstable fracture is found to be consistent with the attainment of a stress intensification close to the tip such that the maximum principal stress σ_yy exceeds σ_f over a characteristic distance, determined as twice the grain size. The model is seen to predict the experimentally determined variation of K_Ic with temperature over the range -150 to -75°C from a knowledge of the yield stress and hardening properties. It is further shown that the onset of fibrous fracture ahead of the tip can be deduced from the position of the maximum achievable stress intensification. The relationship between the model for fracture ahead of a sharp crack, and that ahead of a rounded notch, is discussed in detail.     

Initiation and arrest of cracks on two pipeline steels at low temperature

Dynamic fracture toughness at initiationK _1d and fracture toughness at arrestK _1a were measured on two pipeline steel grades. Dynamic fracture toughness was measured at a very high loading rate with the help of split Hopkinson pressure bars. The values ofK _1d andK _1a are compared. The purpose of this work is to examine the possibilities of using dynamic fracture toughness at crack initiation as a lower bound of crack arrest toughness. This work has practical applications because crack arrest tests are difficult to perform, give scattered results and are costly and time consuming. This procedure shows that it is possible to economize and rationalize using intelligent technology.     

平面应变下紧凑拉伸试样的动态断裂韧性的实验研究

材料的动态断裂韧性是衡量材料在动载荷作用下抵杭裂纹扩展能力的重要指标,以往的材料动态断裂韧性测试多采用三点弯曲试样,而针对紧凑拉伸试样的动态断裂韧性研究很少.本文将紧凑拉伸试样(即CT试样)简化成等效弹簧质量模型,得到了CT试样动态应力强度因子的近似表达式.对Hopkinson压杆装置进行了改进,利用改进后的实验装置进...     

A novel method in determination of dynamic fracture toughness under mixed mode I/II impact loading

The objective of this paper is to propose a novel methodology for determining dynamic fracture toughness (DFT) of materials under mixed mode I/II impact loading. Previous experimental investigations on mixed mode fracture have been largely limited to qusi-static conditions, due to difficulties in the generation of mixed mode dynamic loading and the precise control of mode mixity at crack tip, in absence of sophisticated experimental techniques. In this study, a hybrid experimental–numerical approach is employed to measure mixed mode DFT of 40Cr high strength steel, with the aid of the split Hopkinson tension bar (SHTB) apparatus and finite element analysis (FEA). A fixture device and a series of tensile specimens with an inclined center crack are designed for the tests to generate the components of mode I and mode II dynamic stress intensity factors (DSIF). Through the change of the crack inclination angle β (=90°, 60°, 45°, and 30°), the K_II/K_I ratio is successfully controlled in the range from 0 to 1.14. A mixed mode I/II dynamic fracture plane, which can also exhibit the information of crack inclination angle and loading rate at the same time, is obtained based on the experimental results. A safety zone is determined in this plane according to the characteristic line. Through observation of the fracture surfaces, different fracture mechanisms are found for pure mode I and mixed mode fractures.     

Stress intensity factor and crack velocity relationship for polyester/TiO2 nanocomposites

The dynamic fracture behavior of polyester/TiO₂ nanocomposites has been characterized and compared with that of the matrix material. A relationship between the dynamic stress intensity factor,K _I and the crack tip velocity,å, has been established. Dynamic photoelasticity coupled with high-speed photography has been used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the nanocomposites. Single-edge notch tension and modified compact tension specimens were used to obtain a broad range of crack velocities. Fractographic analysis was conducted to understand the fracture process. The results showed that crack arrest toughness in nanocomposites was 60% greater than in the matrix material. Crack propagation velocities prior to branching in nanocomposites were found to be 50% greater than those in polyester.     

On determination of mode II fracture toughness using semi-circular bend specimen

The cracked semi-circular specimen subjected to three-point bending has been recognized as an appropriate test specimen for conducting mode I, mode II and mixed mode I/II fracture tests in brittle materials. The manufacturing and pre-cracking of the specimen are simple. No complicated loading fixture is also required for a fracture test. However, almost all of the theoretical criteria available for mixed mode brittle fracture fail to predict the experimentally determined mode II fracture toughness obtained from the semi-circular bend (SCB) specimen. In this paper, a modified maximum tangential stress criterion is used for calculating mode II fracture toughness K_IIc in terms of mode I fracture toughness K_Ic. The modified criterion is used for predicting the reported values of mode II fracture toughness for two brittle materials: a rock material (Johnstone) and a brittle polymer (PMMA). It is shown that the modified criterion provides very good predictions for experimental results.     

A Study on the Evaluation of the Fracture Process Zone in CCNBD Rock Samples

The safety of many civil and mining concrete and rock structures including pre-existing crack networks is fundamentally affected by the mechanical behaviour of the material under static and cyclic loading. In cyclic loading case, cracks can grow at a lower load level compared to the monotonic case. This phenomenon is called fatigue due to subcritical crack propagation and depends on the behaviour of the fracture process zone (FPZ). This study presents the results of laboratory diametrical compression tests performed on Brisbane tuff disc specimens to investigate their mode-I (tensile) fracture toughness response to static and cyclic loading and relevant FPZ. The FPZ and fracture toughness response to cyclic loading was found to be different from that under static loading in terms of the ultimate load and the damage mechanisms in front of the chevron crack. A maximum reduction of the static fracture toughness (K _IC ) of 42 % was obtained for the highest amplitude increasing cyclic loading test. Detailed scanning electron microscope (SEM) examinations were performed on the surfaces of the tips of the chevron notch cracks, revealing that both loading methods cause FPZ development in the CCNBD specimens. When compared with monotonic FPZ development, the main difference with the cyclically loaded specimens was that intergranular cracks were formed due to particle breakage under cyclic loading, while smooth and bright cracks along cleavage planes were formed under static loading. Further, the SEM images showed that fatigue damage in Brisbane tuff is strongly influenced by the failure of the matrix because of both intergranular and transgranular subcritical fracturing.     

Mixed Mode Dynamic Fracture in Particulate Reinforced Functionally Graded Materials

A detailed analytical and experimental investigation is presented to understand the dynamic fracture behavior of functionally graded materials (FGMs) under mode I and mixed mode loading conditions. Crack-tip stress, strain and displacement fields for a mixed mode crack propagating at an angle from the direction of property gradation were obtained through an asymptotic analysis coupled with a displacement potential approach. This was followed by a comprehensive series of experiments to gain further insight into the behavior of propagating cracks in FGMs. Dynamic photoelasticity coupled with high-speed photography was used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the FGMs. Dynamic fracture experiments were performed using different specimen geometries to develop a dynamic constitutive fracture relationship between the mode I dynamic stress intensity factor (K _ID ) and crack-tip velocity ( ) for FGMs with the crack moving in the direction of increasing fracture toughness. A similar -K _ID relation was also obtained for matrix material (polyester) for comparison purposes. The results obtained show that crack propagation velocities in FGMs were about 80% higher than the polyester matrix. Crack arrest toughness was found to be about 10% lower than the value of local fracture toughness in FGMs.     

Fatigue crack growth studies in rail steels and associated weld metal

Fatigue crack growth studies in rail steels and associated weld metal have shown that (a) deformed rail steel exhibited fatigue crack growth rates that are slightly faster than undeformed rail steel and (b) weld metal growth data are appreciably faster than rail steel growth results and exhibit growth rate plateaux that reside above the upper bound reported for rail steel fatigue crack growth.In rail steel microstructures at low ΔK levels fatigue crack extension occurred by a ductile striated growth mechanism. However at K_max values approaching 40 MPa √m transgranular cleavage facets initially formed and their incidence increased with K_max until final fast fracture. The average cleavage facet size agreed well with pearlite nodule dimensions of 60–100 μm.The weld metal microstructure was much coarser than the rail steel and contained highly directional columnar grain growth. At all ΔK levels the dominant fracture mode was transgranular cleavage containing small isolated regions of ductile striated fatigue crack growth. The cleavage facet size varied from 150 to 600 μm; such a large variation was explained by the fact that in general crack extension tended to occur in association with the proeutectoid ferrite phase.     

A study of hysteresis in theK ID -å relation

A photoelastic study of high speed crack propagation in Homalite 100 was conducted to measure hysteresis in the constitutive relation forK _ID -å. The fracture specimen was designed to obtain both crack acceleration and deceleration during a single crack extension. Additional loads perpendicular to the cráck-propagation path were applied at secondary locations to accentuate the magnitude of acceleration-deceleration observed in this specimen. The photoelastic data were analyzed using dynamic stress field equations in conjunction with the least-squares over-deterministic method to obtain the crack-propagation fracture toughness,K _ID . Crack velocity, å, was determined numerically by differentiating a polynomial fitted to the crack length-time data in a leastsquares sense. Experimental results indicate that Homalite 100 does not exhibit significant hysteresis in theK _ID -å relation.     

Fracture toughness for CNT specimens from numerically obtained critical CTOD values

Many approaches for estimating mode I fracture toughness (K_IC) using circumferentially notched tensile (CNT) specimen have been demonstrated in the literature. In this paper, an effective approach for estimating fracture toughness from the numerical solution of critical crack tip opening displacement (CTOD) is proposed. An elasto-plastic finite element analysis is used to estimate critical CTOD values for CNT specimens. A number of materials are analysed, and the relationship between K_IC and critical CTOD for CNT specimens is obtained. The proposed relationship is validated by comparing the fracture toughness values obtained from the relationship with those obtained experimentally using CNT specimens. The fracture toughness (K_IC) calculated according to this relationship from numerically obtained critical CTOD is found to be in close agreement with the experimentally obtained fracture toughness for the respective materials.     

Role of inclusion stiffness and interfacial strength on dynamic matrix crack growth: An experimental study

Experimental simulations of dynamic crack growth past inclusions of two different elastic moduli, stiff (glass) and compliant (polyurethane) relative to the matrix (epoxy), are carried out in a 2D setting. Full-field surface deformations are mapped in the crack–inclusion vicinity optically. The crack growth behavior as a function of inclusion–matrix interfacial strength and the inclusion location relative to the crack is studied under stress-wave loading conditions. An ultra high-speed rotating mirror-type digital camera is used to record random speckle patterns in the crack–inclusion vicinity to quantify in-plane displacement fields. The crack-tip deformation histories from the time of impact until complete fracture are mapped and fracture parameters are extracted. The crack front is arrested by the symmetrically located compliant inclusion for about half the duration needed for complete fracture event. The dynamically propagating crack is attracted and trapped by the weakly bonded inclusion interface for both stiff and compliant symmetrically located inclusion cases, whereas it is deflected away by the strongly bonded stiff inclusion and attracted by strongly bonded compliant inclusion when located eccentrically. The crack is arrested by a strongly bonded compliant inclusion for a significant fraction of the total dynamic event and is longer than the one for the weakly bonded counterpart. The compliant inclusion cases show higher fracture toughness than the stiff inclusion cases. Measured crack-tip mode-mixities correlate well with the observed crack attraction and repulsion mechanisms. Macroscopic examination of fracture surfaces reveals much higher surface roughness and ruggedness after crack–inclusion interaction for compliant inclusion than the stiff one. Implications of these observations on the dynamic fracture behavior of micron size A-glass and polyamide (PA6) particle filled epoxy is demonstrated. Filled-epoxy with 3% V_f of PA6 filler is shown to produce the same dynamic fracture toughness enhancement as the one due to 10% V_f glass.     

Mode III effects on interface delamination

For crack growth along an interface between dissimilar materials the effect of combined modes I, II and III at the crack-tip is investigated. First, in order to highlight situations where crack growth is affected by a mode III contribution, examples of material configurations are discussed where mode III has an effect. Subsequently, the focus is on crack growth along an interface between an elastic-plastic solid and an elastic substrate. The analyses are carried out for conditions of small-scale yielding, with the fracture process at the interface represented by a cohesive zone model. Due to the mismatch of elastic properties across the interface the corresponding elastic solution has an oscillating stress singularity, and this solution is applied as boundary conditions on the outer edge of the region analyzed. For several combinations of modes I, II and III crack growth resistance curves are calculated numerically in order to determine the steady-state fracture toughness. For given values of K_I and K_II the minimum fracture toughness corresponds to K_III=0 in most of the range analyzed, but there is a range where the minimum occurs for a nonzero value of K_III.     

The equivalence of K Ic and J Ic fracture-toughness measurements in Ni−Cr−Mo steels

Several series of fracture-toughness measurements were made in 4340 type steels, using both the standardK _Ic test method and theJ _Ic test method described by Landes and Begley.K _Ic results andJ _Ic results converted toK _Ic units are nearly identical for a given steel over a range of specimen size. The fracture toughness of steels produced by vacuum-degassing, remelt, and airmelt processes are compared over a range of yield stress. SimplifiedJ _Ic test procedures are suggested for use with Ni?Cr?Mo steels within certain ranges of yield stress and specimen geometry.     

K Ic and J-resistance-curve measurements on Nevada tuff

Linear-elastic fracture mechanics and J-integral test methods were used to determine the static fracture behavior of a porous volcanic tuff. Notched and prefatigued specimens of two different sizes were tested in three-point bending. The fracture toughness (K _Ic ) and theJ-resistance (J vs. crack growth) curve for each specimen was determined. The results indicate that there is good agreement between the fracture parameters determined by the two methods; however, there is some dependence of the results on specimen size. Possible reasons for this specimen-size dependence are discussed.     

Critique on fracture criteria in mixed-mode-loading

The paper presents an improved formulation of mixed-mode fracture criteria. Both the fracture toughness K_IC and K_IIC are taken into account. Consequently, the crack propagation direction and the fracture envelope in the and plane depends on the toughness ratio . In the plane only one envelope for each criterion is obtained.     

An indentation technique for estimating the energy density as fracture toughness with Berkovich indenter for ductile bulk materials

A technique is proposed to estimate the energy density as fracture toughness for ductile bulk materials with an indentation system equipped with a Berkovich indenter based on the theory of plastic deformation energy transforming into the indentation energy of fracture. With progressive increase of penetration loads, the material damage is exhibited on the effective elastic modulus. A quadratic polynomial relationship between the plastic penetration depth and penetration load, and an approximate linear relationship between logarithmic plastic penetration depth and logarithmic effective elastic modulus are exhibited by indentation investigation with Berkovich indenter. The parameter of damage variable is proposed to determine the critical effective elastic modulus at the fracture point. And the strain energy density factor is calculated according to the equations of penetration load, plastic penetration depth and effective elastic modulus. The fracture toughness of aluminum alloy and stainless steel are evaluated by both indentation tests and K_IC fracture toughness tests. The predicted S_cr values of indentation tests are in good agreement with experimental results of CT tests.     

Effect of specimen size and crack depth on 3D crack-front constraint for SENB specimens

Three-dimensional (3D) elastic–plastic finite element analyses (FEA) are performed to study constraint effect on the crack-front stress fields for single-edge notched bend (SENB) specimens. Both rectangular and square cross-section of the specimens with a deep crack of a/W=0.5 are considered to investigate the effect of specimen size. A square-cross-section specimen with a shallow crack of a/W=0.15 is also considered to examine the effect of crack depth. Stresses from FEA at the crack front on different planes of the specimen are compared with those determined by the J–A₂ three-term solution. Results show that in-plane stress fields can be characterized by the three-term solution throughout the thickness even in the region near the free surface. Cleavage fracture toughness data is compared to predict the effects of specimen size and crack depth on fracture behavior. It is found that the distributions of crack opening stress are nearly the same for the SENB specimens at the critical J which is consistent with the RKR model. Furthermore our results indicate that there is a distinct relationship between the crack-front constraint and the cleavage fracture toughness. By introducing the failure curves, the minimum fracture toughness and scatter band can be well captured using the J–A₂ approach.     

Fracture toughness of CIP-HIP Beryllium at elevated temperatures

The fracture toughness of CIP-HIP Beryllium was determined using the short bar fracture toughness (K_IcSB) method. The K_IcSB value measured was 10.96 MPa√m at room temperature. This falls well within the expected range of 9 to 12 MPa√m as observed from previous fracture toughness measurements of beryllium. Toughness increased rapidly between 400°F and 500°F reaching a value of 16.7 MPa√m at 500°F.