Non-local stress approach to fracture initiation in laboratory experiments with a tensile stress gradient

The paper discusses the stress distribution and the fracturing in diametrically loaded discs in which a hole has been drilled at some distance from the loaded diameter. A linear elastic analysis of the problem indicates that the maximum tensile stress at the hole is up to four times the tensile stress along the loaded diameter. For the configurations in which the tensile stress gradients at the hole are large, the discs nevertheless fail unstably along the loaded diameter, without a sign of fracturing at the hole. A non-local stress approach to fracture initiation satisfactorily explains this behaviour. A similar analysis of fracture initiation on the same type of limestone in other configurations with a stress gradient yields similar values for the characteristic length and for the non-local tensile strength.     

Two neighbouring quasi-trapezoidal holes in discs with minimum s.c.f.

Using a two dimensional photoelastic technique, hole shapes have been optimised in diametrically loaded circular discs with two neighbouring holes leading to minimum stress concentration factor (s.c.f.). Two neighbouring holes symmetrically located side by side with the load axis perpendicular to the line joining the centres of the holes are considered. Results are given for a range of disc diameter/hole diameter ratios (11.44≥D/d≥4.16). Optimised quasi-trapezoidal hole geometries, stress distributions around these holes and the effect of tilting the load direction are presented. In comparison with circular holes, the s.c.fs. have been reduced up to about 14% with quasi-trapezoidal holes at regions of peak stresses and up to 23% at peak tensile stress regions.     

Hole shape optimisation in circular discs with two neighbouring holes

Using a two-dimensional photoelastic technique, hole shapes have been optimised in diametrically loaded circular discs with two neighbouring holes leading to minimum s.c.f. Results are given for a range of disc diameter/hole diameter ratios (15.39 $ D/d $ 3.74). In comparison with circular holes, the s.c.f's have been reduced upto about 21 per cent at regions where peak stresses act. The results include the stress distribution around the holes, optimum geometries developed and the effect of tilting the load direction.     

The dependence of the strength of zinc sulphide on temperature and environment

The dependence of the strength of zinc sulphide on temperature, environment, surface finish and specimen size has been assessed. Room-temperature fracture stresses were determined using a bursting disc geometry for a number of different surface finishes and for two different sample sizes. High and low-temperature fracture stresses in a dry nitrogen atmosphere were obtained from experiments using the Brazilian test geometry and showed that the average strength of the material remained above or equal to the room-temperature value within the range –70 to +600 °C. The Brazilian test is an indirect tensile technique which is attractive for its experimental simplicity but gives fracture stress values which are consistently below those obtained by direct tensile techniques. The data from this test were therefore compared at room temperature to results obtained from the bursting disc test on samples which had been prepared using the same techniques. The possibility of delayed failure through environmentally enhanced slow crack growth was evaluated using the double-torsion technique which revealed slow crack growth below the critical stress intensity factor.     

Investigation of proper specimen geometry for mode I fracture toughness testing with flattened Brazilian disc method

Investigation of geometrical parameters for flattened Brazilian disc method is important, since this is a simple and attractive method for mode I fracture toughness testing on rock cores. Evaluating numerical modeling results, a parametric equation in terms of principal stresses at the center of the disc and the loading angle of the flattened end was developed. An equation was proposed for maximum stress intensity factors at critical crack lengths around stable to unstable crack propagation. Comparing fracture toughness results of flattened Brazilian disc method to the results of the suggested cracked chevron notched Brazilian disc method, geometrical parameters for flattened Brazilian discs were investigated. Diameter, loading angle of flattened ends, and thickness of andesite rock core specimens were changed to obtain comparable results to the suggested method. The closest results to the suggested method were obtained by 54 mm diameter discs with loading angles larger than 32°, and thicknesses between 19 and 34 mm. Results were confirmed by the flattened Brazilian disc tests on a marble rock. In flattened Brazilian disc tests with smaller loading angles and larger diameters, larger fracture toughness values than the results of the suggested cracked chevron notched were obtained. However, excluding tests with large loading angles over 27°; specimen size was less effective on the results of these tests. Critical crack length parameters computed from modeling and experiments were close to each other for the flattened Brazilian disc specimens with smaller loading angles around 20° and thickness/radius ratio equal or less than 1.1.     

The dispersion of birefringence in photoelastic materials

A spectral analyser was used to determine the variation with wavelength known as the dispersion of birefringence of the fringe constant f and the stress optic coefficient C for photoelastic materials. A disc was loaded diametrically and was subjected to the stress freezing thermal cycle. The intensity was measured along the diameter perpendicular to the load for wavelengths between 450 and 850 nm at 5 nm intervals. Using the theoretical solution to the stresses it was possible to calculate the stress optic coefficient for all wavelengths employed. A similar technique was used for an identical disc that was loaded at room temperature. It was found that the fringe constant was extremely linear with wavelength for both types of loading and for the materials CT200, CT1200 and MY750. The stress optic coefficient did not change much between sheets of the same material but was markedly different between materials. The dispersion of birefringence was found to be approximately constant but showed evidence of anomalous dispersion.     

Tensile fracture of doubly-convex cylindrical discs under diametral loading

Doubly-convex cylindrical gypsum discs have been fractured under the action of two diametrically opposed in-plane forces. The disc diameter was constant throughout the test series. The ratio of cylinder length to diameter ranged from 0.06 to 0.30; the ratio of cylinder diameter to radius of curvature of the disk faces was varied from 0 to 1.43. The fracture loads obtained have been correlated with stress data obtained from the photoelastic analysis of Pitt et al. An empirical equation, valid for any brittle material, relating the tensile strength of the material to the fracture load and dimensions of a doubly-convex disc has also been developed.Nomenclature C, K constants - D diameter of disc - F comparative factor - I _max stress factor - P load - P _s fracture load of convex-faced disc - P ₂ fracture load of plane-faced disc with W/D = 0.2 - R radius of face-curvature - t overall thickness of convex-faced disc - T thickness of plane-faced specimen of convexfaced disc - W cylinder length - _f tensile strength of material - _t maximum tensile stress in convex-faced disc - _x uniform tensile stress in plane-faced disc     

Modelling of crack propagation in rocks under SHPB impacts using a damage method

Rock dynamic fracture is a complex problem and has received considerable attention during the last few decades. In this paper, tensile crack softening failure criterion is used to study impact‐induced crack initiation and propagation in rocks. In order to examine applicability of the criterion, under realistic loading and boundary conditions, three boundary conditions were analyzed in details and an impacting experiment using single cleavage semicircle compression (SCSC) specimens had been successfully simulated. A good agreement was achieved between the simulation and experimental results. It was concluded that the boundary conditions play an important role in rock dynamic fracturing. When a stress wave propagates from a material with low wave impedance to a material of high wave impedance, the compression wave is partially reflected back and the process of fast cracking is suppressed. In addition, with the change of the tensile strength and the fracture energy, the crack initiation modes can be divided into four types.     

Untersuchung der Rißbildung in Salzgestein mit Hilfe der Schallemissionsanalyse

Acoustic Emission Measurements During Hydraulic Fracturing Tests in Rock salt To investigate the state of stress in the rock, during a hydraulic fracturing experiment the hydraulic pressure in a sealed volume of a borehole is increased up to the initiation of a fracture. In this paper hydraulic fracturing experiments are described which were performed in the salt rock of the former Asse salt mine and in a laboratory specimen of 200mm diameter. Acoustic Emission measurements were applied to evaluate the three-dimensional orientation and the extension of the fracture area. A multi-channel signal analysis system was used. The results correlate fairly well with the fracture locations which were surveyed after the experiments.     

用应变片法确定混凝土动态起裂时间的研究

在混凝土等准脆性材料的动态起裂韧度K_(1d)测试中,准确确定试件裂尖的起裂时间是测试工作的关键。采用分离式霍普金森压杆系统,对圆孔裂纹平台巴西圆盘混凝土试件进行动态径向冲击试验,通过在裂尖粘贴应变片的方法来确定起裂时间。讨论了应变片在裂纹尖端的粘贴位置、粘贴方向等因素对起裂时间测试值的影响,结果表明裂尖应变片的最佳粘贴方式是:在裂纹延长线上或在裂尖并与裂纹垂直的线上,都距离裂尖3 mm左右,且粘贴方向与裂纹延长线垂直。给出了考虑贴片位置和试件厚度的起裂时间计算公式。