An analytical model of multi-stress drops triggered by localized microcrack damage in brittle rocks during progressive failure

2020 ◽  
Vol 29 (9) ◽  
pp. 1345-1360
Author(s):  
Xiaozhao Li ◽  
Xiaolei Qu ◽  
Chengzhi Qi ◽  
Zhushan Shao
Keyword(s):  
Theoretical Model ◽  
Axial Strain ◽  
Wing Crack ◽  
Underground Engineering ◽  
Stress Strain ◽  
Brittle Rocks ◽  
Deep Underground ◽  
Earthquake Mechanism ◽  
Microcrack Growth ◽  
Stress Drops

Stress drops in stress–strain constitutive curves of intact brittle rocks under high confining pressure have great significance for evaluating the earthquake mechanism and the safety of deep underground engineering. Microcrack growth in intact rock strongly influences the stress drops. However, the theoretical model of microcrack growth-dependent multi-stress drops rarely is proposed in stress–strain curves of intact rocks. In this study, a constitutive model depending on the damage variable relating to microcrack growth and strain increment is proposed to explain the multi-stress drops in stress–strain curves including strain hardening and softening phases of intact rocks. This model is formulated by combining the wing crack growth model, the suggested relationship between axial strain and wing crack growth, and the stepping function of damage relating to axial strain. This stepping function of damage relating to axial strain approximately is used to simulate the developing process of the small individual shear bands caused by the local microcrack accumulation and coalescence. The effects of parameters in the suggested stepping function of damage on the stress–strain curves containing stress drops are discussed. The theoretical model qualitatively explains the experimental phenomena of multi-stress drops in the stress–strain curves, which provides an important implication for evaluating the earthquake mechanism and the safety of deep underground engineering.

scholarly journals A Macro–Micro Damage Model for Rock under Compression Loading

2021 ◽  
Vol 11 (24) ◽  
pp. 12154
Author(s):  
Zhixiong Peng ◽  
Yawu Zeng ◽  
Xi Chen ◽  
Shufan Cheng
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Damage Model ◽  
Compressive Loading ◽  
Calculation Model ◽  
Wing Crack ◽  
Stress Strain ◽  
Sandstone Sample ◽  
Microcrack Growth

Rock damage caused by its microcrack growth has a great influence on the deformation and strength properties of rock under compressive loading. Considering the interaction of wing cracks and the additional stress caused by rock bridge damage, a new calculation model for the mode-I stress intensity factor at wing crack tip was proposed in this study. The proposed calculation model for the stress intensity factor can not only accurately predict the cracking angle of wing crack, but can also simulate the whole range of variation of wing crack length from being extremely short to very long. Based on the modified stress intensity factor, a macro–micro damage model for rock materials was also established by combining the relationship between microcrack growth and macroscopic strain. The proposed damage model was verified with the results from the conventional triaxial compression test of sandstone sample. The results show that the proposed damage model can not only continuously simulate the stress-strain curves under different confining pressures, but also can better predict the peak strength. Furthermore, the sensitivities of initial crack size, crack friction coefficient, fracture toughness, initial damage and parameter m on the stress-strain relationship are discussed. The results can provide a theoretical reference for understanding the effect of microcrack growth on the progressive failure of rock under the compressive loading.

Combined-Stress Tests on 24S-T Aluminum-Alloy Tubes

1947 ◽  
Vol 14 (2) ◽  
pp. A147-A153
Author(s):  
W. R. Osgood
Keyword(s):  
Aluminum Alloy ◽  
Hoop Stress ◽  
Axial Stress ◽  
Axial Strain ◽  
Maximum Deviation ◽  
Shearing Stress ◽  
Stress Tests ◽  
Combined Stress ◽  
Stress Strain ◽  
Shearing Strain

Abstract Combined-stress tests were made on five 24S-T aluminum-alloy tubes, 1 3/4 in. ID × 0.05 in. thick. The ratios of circumferential (hoop) stress to axial stress were 0, 1/2, 1, 2, and ∞. The tubes were tested to failure and sufficient measurements of circumferential strain and axial strain were taken to plot stress-strain curves almost up to rupture. The results are presented in the form of two sets of stress-strain curves for each ratio of stresses, namely, maximum shearing stress plotted against maximum shearing strain, and octahedral shearing stress plotted against octahedral shearing strain. In each plot the maximum deviation of the curves is about ± 5 per cent. A method of evaluating small octahedral shearing strains from the data is given which does not assume Poisson’s ratio to be 1/2.

Prediction of Stress-Strain Response Using Rotational Multiple Yield Surface Framework in Malaysian Residual Soil

2020 ◽  
Vol 843 ◽  
pp. 132-137
Author(s):  
Asmidar Alias ◽  
Mohd Jamaludin Md Noor ◽  
Abdul Samad Abdul Rahman
Keyword(s):  
Shear Strength ◽  
Effective Stress ◽  
Volume Change ◽  
Yield Surface ◽  
Axial Strain ◽  
The Body ◽  
Residual Soil ◽  
Strain Response ◽  
Stress Strain ◽  
Soil Volume

Soil settlement is normally quantified using conventional soil volume change models which are solely based on the effective stress and the role of shear strength is ignored due to the difficulties to incorporate in the framework. The Rotational Multiple Yield Surface Framework (RMYSF) is a soil volume change model developed from the standpoint of the interaction between the effective stress and shear strength. RMYSF incorporates the development of mobilised shear strength within the body of the soil whenever the soil is subjected to anisotropic compression. Currently the framework has been applied to predict the soil anisotropic stress-strain behaviour at any effective stress. This paper present the enhancement of this volume change framework using normalisation of axial strain with the understanding that the failure axial strain is not unique, but increases as the effective stress increases. This technique has essentially produced a better accuracy in the prediction of the stress-strain response for Malaysian residual soils. A series of drained tri-axial tests under various effective stresses has been conducted using specimens of 50mm diameter and 100mm height and from the stress-strain curves the inherent mobilised shear strength envelopes at various axial strains have been determined. These mobilised shear strength envelopes were then applied for the prediction of the soil stress-strain response. An excellent agreement between the predicted and the actual stress-strain curves has been achieved.

Comparison of Stress-Strain Relationships of FRP and Actively Confined High-Strength Concrete: Experimental Observations

2014 ◽  
Vol 919-921 ◽  
pp. 29-34 ◽  
Author(s):  
Jian Chin Lim ◽  
Togay Ozbakkloglu
Keyword(s):  
High Strength Concrete ◽  
Axial Stress ◽  
Axial Strain ◽  
High Strength ◽  
Confining Pressure ◽  
Confined Concrete ◽  
Lateral Strain ◽  
Stress Strain ◽  
Strength Concrete ◽  
Actively Confined Concrete

It is well established that lateral confinement of concrete enhances its axial strength and deformability. It is often assumed that, at a same level of confining pressure, the axial compressive stress and strain of fiber reinforced polymer (FRP)-confined concrete at a given lateral strain are the same as those in concrete actively confined concrete. To assess the validity of this assumption, an experimental program relating both types of confinement systems was conducted. 25 FRP-confined and actively confined high-strength concrete (HSC) specimens cast from a same batch of concrete were tested under axial compression. The axial stress-strain and lateral strain-axial strain curves obtained from the two different confinement systems were assessed. The results indicate that, at a given axial strain, lateral strains of actively confined and FRP-confined concretes correspond, when they are subjected to the same lateral confining pressure. However, it is observed that, at these points of intersections on axial strain-lateral strain curves, FRP-confined concrete exhibits a lower axial stress than the actively confined concrete, indicating that the aforementioned assumption is not accurate. The test results indicate that the difference in the axial stresses of FRP-confined and actively confined HSC becomes more significant with an increase in the level of confining pressure.

A Model to Predict the Effect of Pre-Strain on the Fracture Toughness of Line Pipe Steel

2002 ◽  
Author(s):  
Andrew Cosham ◽  
Naoto Hagiwara ◽  
Naoki Fukuda ◽  
Tomoki Masuda
Keyword(s):  
Fracture Toughness ◽  
Plastic Deformation ◽  
Theoretical Model ◽  
Plastic Strain ◽  
Ductile Fracture ◽  
Experimental Studies ◽  
Uniaxial Tensile ◽  
Stress Strain ◽  
Line Pipe ◽  
Strained Material

New and existing pipelines can be subjected to high plastic strains. Denting a pipeline causes permanent plastic deformation. Onshore pipelines subject to subsidence, frost heave or earthquake loading can experience significant plastic strain during service. Offshore pipelines that are reeled prior to laying, or are laid in deep water, or are operating at high temperatures and high pressures, can experience significant plastic strain both prior to, and during, service. Experimental studies have indicated that pre-strain (permanent plastic deformation) has a detrimental effect on the fracture toughness of steel; it reduces the resistance to crack initiation, reduces the resistance to crack growth, and increases the transition temperature. Consequently, there is a need for a thorough understanding of the effect of pre-strain on the fracture toughness of line pipe. Accordingly, a theoretical model for predicting the effect of tensile pre-strain on the ductile fracture toughness has been developed using the local approach. The effect of pre-strain is expressed in terms of an equation for the ratio of the fracture toughness of the pre-strained material to that of the virgin (not pre-strained) material. The model indicates that the effect of tensile pre-strain on the material’s fracture toughness can be characterised in terms of the effect of pre-strain on the stress-strain characteristics of the material, the critical fracture strain for a stress state corresponding to that during pre-strain, and several parameters that relate to the conditions for ductile fracture (or cleavage fracture). The implications of the model are that it may be possible to estimate the reduction in toughness caused by pre-strain simply from a full stress-strain curve of the virgin material. The model has been validated against the results of crack tip opening displacement (CTOD) tests conducted by Tokyo Gas on two line pipe steels subject to uniaxial tensile pre-strain. It is shown that the predictions and trends of the theoretical model are in broad agreement with the test results.

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