Determination of dynamic rock Mode-I fracture parameters using cracked chevron notched semi-circular bend specimen

Rock dynamic fractures are common in many geophysical processes and engineering applications. Characterization of rock dynamic fracture properties such as the initiation fracture toughness, the fracture energy, and the fracture velocity, is thus of great importance in rock mechanics. A novel method is proposed in this work to measure dynamic Mode-I rock fracture parameters using a cracked chevron notched semi-circular bend (CCNSCB) specimen loaded by a split Hopkinson pressure bar (SHPB) apparatus. A strain gauge is mounted on the sample surface near the chevron notch to detect the fracture onset, and a laser gap gauge (LGG) is used to monitor the crack surface opening distance (CSOD) during the dynamic test. With dynamic force balance achieved in the tests, the stable–unstable transition of the crack propagation crack is observed and the initiation fracture toughness is calculated from the dynamic peak load. The average dynamic fracture energy as well as the fracture propagation toughness are calculated based on the first law of thermodynamics. The measured dynamic fracture properties of Laurentian granite using CCNSCB method are consistent with those reported in the literature using other methods.     

Quasi-static and dynamic fracture initiation toughness of Ti/TiB layered functionally graded material under thermo-mechanical loading

Quasi-static and dynamic fracture initiation toughness of Ti/TiB layered functionally graded material (FGM) is investigated using a three point bend specimen. The modified split Hopkinson pressure bar (SHPB) apparatus in conjunction with induction coil heating system is used during elevated temperature dynamic loading experiments. A simple and accurate technique has been developed to identify the time corresponding to the load at which the fracture initiates. A series of experiments are conducted at different temperatures ranging from room temperature to 800 °C, and the effect of temperature and loading rate on the fracture initiation toughness is investigated. The material fracture toughness is found to be sensitive to temperature and the fracture initiation toughness increases as the temperature increases. Furthermore, the fracture initiation toughness is strain rate sensitive and is higher for dynamic loading as compared to quasi-static loading.     

冲击载荷下岩石材料动态断裂韧性测试研究进展

岩石动态断裂韧性是岩石动力学的基本力学参数之一,也是评价岩石抵抗裂纹动态起裂和扩展性能的重要参数之一。随着采矿工程、岩土工程的不断发展,冲击动态载荷下岩石动态断裂韧性的研究也愈来愈为国内外岩土工程界所关注。综述了冲击载荷下岩石材料动态断裂韧性测试研究进展,主要介绍了冲击载荷下岩石动态断裂韧性测试技术研究成就及其优缺点,并就冲击载荷下岩石动态断裂韧性测试研究发展趋势给予展望。     

J55套管的断裂韧性

研究了两种Ｊ５５套管的动，静态断裂韧性，表明以静态断裂韧性计算动态断裂韧性是可行的，试验结果也表明动态下材料的脆化倾向增强，动态断裂韧性Ｋ１ｄ明显低于静态Ｋ。     

半圆盘构件冲击断裂特性的动态焦散线实验研究

采用动态焦散线实验系统,对有机玻璃（PMMA）在冲击载荷下的I型和I-II混合型裂纹在起裂和扩展时的动态断裂特性进行了研究。结果表明：随着PMMA由I型断裂转变为I-II混合型断裂,从落锤作用在试件上到裂纹起裂所需时间不断增加,说明裂纹起裂需要的能量有所增加,同时从裂纹起裂到最终贯通所需时间不断减少,说明裂纹平均扩展速度也不断增大;在I型断裂中,PMMA的断裂韧度KIC为2.04 MN/m3/2,而在I-II混合型断裂中,PMMA的断裂韧度KIC低于I型断裂时的断裂韧度KIC,但是KIIC有所增大;对于I-II混合型断裂,PMMA极限扩展速度约为366m/s,当达到极限扩展速度后,裂纹尖端出现微裂纹增韧现象,使裂纹的表面能迅速增大,随后裂纹的扩展速度迅速减小。     

预加载下岩石的动态力学性能研究

动态和静态载荷共同作用下的岩石力学特性是深部地下岩石工程的关键问题。设计了用于测试静态预加载下岩石动态力学性能的分离式霍普金森压杆系统,并详细介绍了具有预加载装置的分离式霍普金森压杆系统的原理、数据分析和应力波的传播过程。通过具有预加载装置的分离式霍普金森压杆系统研究了岩石在不同预拉伸应力下的拉伸强度。结果表明:动态拉伸强度和总拉伸强度随着加载率的增加而增加,同时,在相同加载率下,动态拉伸强度随着预拉伸载荷的增加而减小,而总拉伸应力与预拉伸载荷的大小无关。此外,对不同预加载条件下岩石的动态断裂韧度也进行了研究,实验结果说明岩石的动态断裂韧度和总断裂韧度随着加载率的增加而增加。在相同加载率下,动态断裂韧度随着预加载荷的增加而减小,而总断裂韧度随着加载率的增加而增加。     

An experimental cum numerical technique to determine dynamic interlaminar fracture toughness

A method combining experimental and finite element analysis is developed to determine interlaminar dynamic fracture toughness. An interlaminar crack is propagated at very high speed in a double cantilever beam (DCB) specimen made of two steel strips which are bonded together by epoxy with a precrack of about 40 mm length. The face of the front cantilever is bonded to a large solid block and a special fixture is designed to apply impact load to the rear cantilever through a load bar. In the load bar, a compressive square shaped elastic stress pulse is generated by impacting it with a striker bar which is accelerated in an air gun. The rear cantilever is screwed to the load bar; when the incident compressive pulse reaches the specimen, a part of the energy is reflected into the load bar and the rest of it passes to the specimen. By monitoring the incident and the reflected pulses in the load bar through strain gauges, deflection of cantilever-end is determined. The crack velocity is determined by three strain gauges of 0.2 mm gauge length bonded to the side face of the rear cantilever. Further, the first strain gauge, bonded very close to the tip of the precrack, and the crack velocity determine the initiation time of crack propagation.

The experimental results are used as input data in a finite element (FE) code to calculate J-integral by the gradual release of nodal forces to model the propagation of the interlaminar crack. The initiation fracture toughness and propagation fracture toughness are evaluated for an interlaminar crack propagating with a velocity in the range of 850 to 1785 m/s. The initiation toughness and propagation toughness were found to vary between 90–200 J/m² and 2–13 J/m², respectively.     

Dynamic crack initiation toughness of 4340 steel at constant loading rates

Determination of fracture toughness for metals under quasi-static loading conditions can follow well-established procedures and ASTM standards. The use of metallic materials in impact related applications requires the determination of dynamic crack initiation toughness for these materials. There are two main challenges in experiment design that must be overcome before valid dynamic data can be obtained. Dynamic equilibrium over the entire specimen needs to be approximately achieved to relate the crack tip loading state to the far-field loading conditions, and the loading rate at the crack tip should be maintained near constant during an experiment to delineate rate effects on the values of dynamic crack initiation toughness. A recently developed experimental technique for determining dynamic crack initiation toughness of brittle materials has been adapted to measure the dynamic crack initiation toughness of high-strength steel alloys. A Kolsky pressure bar is used to apply the dynamic loading. A pulse shaper is used to achieve constant loading rate at the crack tip and dynamic equilibrium across the specimen. A four-point bending configuration is used at the gage section of the setup. Results are presented which show a monotonically increasing rate dependence of crack initiation toughness for 4340 high-strength steel.     

Study of mode I crack dynamic propagation behaviour and rock dynamic fracture toughness by using SCT specimens

To study crack dynamic propagation behaviour and rock dynamic fracture toughness, a single cleavage triangle (SCT) specimen was proposed in this paper. By using these specimens and a drop‐weight test system, impact experiments were conducted, and the crack propagation velocity and the fracture time were measured by using crack propagation gauges. To examine the effectiveness of the SCT specimen and to predict the test results, finite difference numerical models were established by using AUTODYN code, and the simulation results showed that the crack propagation path agrees with the test results, and crack arrest phenomena could happen. Meanwhile, by using these numerical models, the crack dynamic propagation mechanism was investigated. Finite element code ABAQUS was applied in the calculation of crack dynamic stress intensity factors (SIFs) based on specimen dimension and the loading curves measured, and the curves of crack dynamic SIFs versus time were obtained. The fracture toughness (including initiation toughness and propagation toughness) was determined according to the fracture time and crack speeds measured by crack propagation gauges. The results show that the SCT specimen is applicable to the study of crack dynamic propagation behaviour and fracture toughness, and in the process of crack propagation, the propagation toughness decreases with crack propagation velocity, and the crack arrest phenomena could happen. The critical SIF of an arrest crack (or arrest toughness) was higher than the crack propagation toughness but was lower than the initiation toughness.     

Quasi-static and dynamic fracture behaviour of rock materials: phenomena and mechanisms

An experimental investigation is conducted to study the quasi-static and dynamic fracture behaviour of sedimentary, igneous and metamorphic rocks. The notched semi-circular bending method has been employed to determine fracture parameters over a wide range of loading rates using both a servo-hydraulic machine and a split Hopkinson pressure bar. The time to fracture, crack speed and velocity of the flying fragment are measured by strain gauges, crack propagation gauge and high-speed photography on the macroscopic level. Dynamic crack initiation toughness is determined from the dynamic stress intensity factor at the time to fracture, and dynamic crack growth toughness is derived by the dynamic fracture energy at a specific crack speed. Systematic fractographic studies on fracture surface are carried out to examine the micromechanisms of fracture. This study reveals clearly that: (1) the crack initiation and growth toughness increase with increasing loading rate and crack speed; (2) the kinetic energy of the flying fragments increases with increasing striking speed; (3) the dynamic fracture energy increases rapidly with the increase of crack speed, and a semi-empirical rate-dependent model is proposed; and (4) the characteristics of fracture surface imply that the failure mechanisms depend on loading rate and rock microstructure.     

INTERFACIAL CRACK INITIATION UNDER QUASI-STATIC AND DYNAMIC LOADING CONDITIONS: AN EXPERIMENTAL STUDY

Abstract— Interfacial fracture parameters under quasi-static and dynamic loading are examined in a large elastic mismatch bimatenal system. A wide range of remote field loading ratios of shear and tension are considered. The crack tip fields are mapped using the optical method of coherent gradient sensing or CGS and fracture parameters are quantified. Distinctly different crack initiation responses are observed for positive and negative shear stresses acting on the interface. Also, low velocity impact loading experiments are conducted to study the influence of dynamic loading on crack initiation parameters. Dynamic interfacial crack tip fields are recorded using high speed photography and fracture parameters for dynamically loaded stationary cracks are obtained. Measurements suggest significant crack initiation toughness reduction under dynamic loading conditions.     

Effect of loading rate on dynamic fracture initiation toughness of brittle materials

Numerical simulation is carried out to investigate the effect of loading rate on dynamic fracture initiation toughness including the crack-tip constraint. Finite element analyses are performed for a single edge cracked plate whose crack surface is subjected to uniform pressure with various loading rate. The first three terms in the Williams’ asymptotic series solution is utilized to characterize the crack-tip stress field under dynamic loads. The coefficient of the third term in Williams’ solution, A ₃, was utilized as a crack tip constraint parameter. Numerical results demonstrate that (a) the dynamic crack tip opening stress field is well represented by the three term solution at various loading rate, (b) the loading rate can be reflected by the constraint, and (c) the constraint A ₃ decreases with increasing loading rate. To predict the dynamic fracture initiation toughness, a failure criterion based on the attainment of a critical opening stress at a critical distance ahead of the crack tip is assumed. Using this failure criterion with the constraint parameter, A ₃, fracture initiation toughness is determined and in agreement with available experimental data for Homalite-100 material at various loading rate.     

Initiation, propagation and arrest of an interface crack subjected to controlled stress wave loading

An experimental study has been conducted to investigate the initiation, propagation, and arrest of bimaterial interface cracks subjected to controlled stress wave loading in the form of a tensile dilatational stress wave pulse. The tensile pulse is generated by detonating lead azide explosive in a specially designed specimen. Dynamic loading of the bimaterial interface results in crack initiation, propagation, and arrest, all in the same experiment. This failure event is observed using photoelasticity in conjunction with high speed photography. Full field data from the experimentally obtained isochromatic fringe patterns is analyzed to determine time histories of various fracture parameters such as the crack tip speed, the dynamic complex stress intensity factor, the energy release rate, and the mixity. The experimental data is also used to quantify the values of the dynamic initiation and arrest toughness and to evaluate a recently proposed dynamic interface fracture criterion. This revised version was published online in August 2006 with corrections to the Cover Date.     

Statistical scatter in the fracture toughness and Charpy impact energy of pearlitic steel

The effect of microstructure on the fracture characteristics of high carbon hypo eutectoid steel was studied under conditions of quasistatic and dynamic loading. Experimentally determined sets of fracture toughness and Charpy impact energy values were statistically treated. A relationship was found between fracture toughness and Charpy impact energy. In the very brittle domain, the fracture toughness increases slightly with increasing Charpy impact energy. In the domain where the fracture toughness is higher, the rise in fracture toughness with increasing Charpy impact energy is more pronounced. Detailed SEM examination of fractured compact tension (CT) and Charpy V-notch (CVN) specimens showed that the fracture at ambient temperature occurred almost exclusively by cleavage. There were no visible differences in the morphology of cleavage facets on the fracture surfaces of Charpy and CT specimens. Mechanisms of cleavage initiation were revealed by the fractographical investigation of fracture surfaces. Whereas the fracture surfaces of broken CT specimens exhibit a number of cleavage origins, the fracture surfaces of CVN specimens usually show only one.     

A model for the dynamic fracture toughness of ductile structural steel

We assume in this paper that the dynamic fracture toughness K_Id of ductile structural steels is dependent on void nucleation and void growth. The void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g were obtained by modifying the void nucleation-induced and void growth-induced static fracture toughness models, respectively, considering the effect of strain rate and local temperature. By the relationship between the void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g((K_Id)²=(K_Id·n)²+(K_Id·g)²) dynamic fracture toughness K_Id could be quantitatively evaluated. With this model the dynamic fracture toughness of two structural steels (X65 and SA440) was assessed, and the causes for the differences between the static and dynamic fracture toughness were also discussed.     

Modelling ductile fracture behaviour from deformation parameters in HSLA steels

In this work, an attempt is made to model the ductile fracture behaviour of two Cu‐strengthened high strength low alloy (HSLA) steels through the understanding of their deformation behaviour. The variations in deformation behaviour are imparted by prior deformation of steels to various predetermined strains. The variations in parameters such as yield strength and true uniform elongation with prior deformation is studied and was found to be analogous to that of initiation fracture toughness determined by independent method. A unique method is used to measure the crack tip deformation characterized by stretch zone depth that also depicted a similar trend. Fracture toughness values derived from the stretch zone depth measurements were found to vary in the same fashion as the experimental values. A semiempirical relationship for obtaining ductile fracture toughness from basic deformation parameters is derived and model is demonstrated to estimate initiation ductile fracture toughness accurately.     

A method for testing interlaminar dynamic fracture toughness of polymeric composites

Static and dynamic Mode I delamination fracture in two polymeric fiber composites was studied using a WIF test method. The dynamic test was conducted on a Split Hopkinson Pressure Bar apparatus. Crack speeds up to 1000 m/s were achieved. Dynamic fracture and crack propagation were modeled by the finite element method. Dynamic initiation fracture toughness of S2/8552 and IM7/977-3 composites were obtained. The dynamic fracture toughness of IM7/977-3 associated with the high speed propagating crack was extracted from the finite element simulation based on the measured data. It was found that the dynamic fracture toughness of the delamination crack propagating at a speed up to 1000 m/s approximately equals the static fracture toughness.     

Rate effects on the mechanical response of magnesium aluminate spinel

The uniaxial compressive, biaxial flexural strength and fracture toughness of a polycrystalline transparent MgAl₂O₄ spinel were characterized over a wide range of loading rates. The flexural tests were carried out by means of ring-on-ring equibiaxial bending, while the fracture toughness was determined by four-point bending on samples with Chevron notch (CN) configuration. The surface crack (SC) method was also attempted in determining the fracture toughness. Quasi-static experiments were conducted on a servohydraulic testing machine, while the high-rate experiments were performed on a modified Kolsky bar. Results showed that both the failure strength and fracture toughness of the spinel were rate sensitive. Edge beveling in sample preparation did not affect the ring-on-ring flexural strength significantly, and the failure initiation sites were found to be inside the loading ring area regardless of edge conditions. Fracture toughness tests following ASTM standard were largely affected by the inherent coarse microstructure of this material.     

霍普金森杆冲击压缩单裂纹圆孔板的岩石动态断裂韧度试验方法

对压缩单裂纹圆孔板(single cleavage drilled compression--SCDC)砂岩试样,利用分离式霍普金森压杆(SHPB)冲击加载,进行了岩石张开型(I型)动态断裂实验。分别采用2种方法确定砂岩的动态断裂韧度,第1种方法是实验-数值法:由SHPB弹性杆上应变片获得作用在试件上的加载力,然后输入有限元分析程序求得试样裂尖动态应力强度因子,对应于裂尖起裂时刻的动态应力强度因子即为材料动态断裂韧度值;第2种方法是准静态法:将载荷峰值代入静态应力强度因子公式确定动态断裂韧度。2种方法的结果差异较大,对无量纲裂纹长度a/R= 0.64(A组)试样,准静态方法确定的断裂韧度值要比实验-数值法确定的断裂韧度值平均要小35%~62%;对无量纲裂纹长度a/R=1.61(B组)试样,准静态方法的计算结果比实验-数值法的计算结果平均要小72%~83%。从原理上讲,实验-数值法比准静态法能更合理地测定岩石的动态断裂韧度。     

Transferability of Charpy Absorbed Energy to Fracture Toughness Based on Weibull Stress Criterion

The relationship between Charpy absorbed energy and the fracture toughness by means of the (crack tip opening displacement (CTOD)) method was analyzed based on the Weibull stress criterion. The Charpy absorbed energy and the fracture toughness were measured for the SN490B steel under the ductile-brittle transition temperature region. For the instrumented Charpy impact test, the curves between the loading point displacement and the load against time were recorded. The critical Weibull stress was taken as a fracture controlled parameter, and it could not be affected by the specimen configuration and the loading pattern based on the local approach. The parameters controlled brittle fracture are obtained from the Charpy absorbed energy results, then the fracture toughness for the compact tension (CT) specimen is predicted. It is found that the results predicted are in good agreement with the experimental. The fracture toughness could be evaluated by the Charpy absorbed energy, because the local approach give