Identifying crack initiation stress threshold in brittle rocks using axial strain stiffness characteristics

As an estimate for the in-situ spalling strength around massive underground excavations to moderately jointed brittle rocks, crack initiation stress marks the initiation of rock micro fracturing. It is crucial to accurately identify crack initiation stress level by proper method. In this study, confined compression tests of sandstone samples are used to examine the validity/applicability of proposed axial strain stiffness method. The results show that by highlighting the minuscule changes in stress-strain curve, the axial strain stiffness curve provided further insight into rock failure process and revealed five stages:(a) irregular fluctuation,(b) nearly horizontal regular fluctuation,(c) irregular fluctuation gradually decreasing to zero,(d) extreme fluctuation, and(e) near zero, which mainly correspond to five stages of stress–strain curve. The ratio of crack-initiation stress to peak strength determined using this approach is 0.44–0.51, similar to the ranges previously reported by other researchers. In this method, the key is to accurately detect the end point of the stage(b), "nearly horizontal regular fluctuation" characterized by a sudden change in axial strain stiffness curve, and the sudden change signifies crack initiation in rock sample. Finally, the research indicates that the axial strain stiffness curve can provide a mean to identify the crack-initiation stress thresholds in brittle rocks.

Crack initiation stress and strain of jointed rock containing multi-cracks under uniaxial compressive loading: A particle flow code approach

The ratio of crack initiation stress to the uniaxial compressive strength(SCI,B/SUC,B) and the ratio of axial strain at the crack initiation stress to the axial strain at the uniaxial compressive strength(B,UCB,CI,A,A/SSSS) were studied by performing numerical stress analysis on blocks having multi flaws at close spacing's under uniaxial loading using PFC3 D. The following findings are obtained: SCI,B/SUC,B has an average value of about 0.5 with a variability of ± 0.1. This range agrees quite well with the values obtained by former research. For joint inclination angle, β=90°,B,UCB,CI,A,A/SSSS is found to be around 0.48 irrespective of the value of joint continuity factor, k. No particular relation is found betweenB,UCB,CI,A,A/SSSS and β; however, the average B,UCB,CI,A,A/SSSS seems to slightly decrease with increasing k. The variability ofB,UCB,CI,A,A/SSSS is found to increase with k.Based on the cases studied in this work,B,UCB,CI,A,A/SSSS ranges between 0.3 and 0.5. This range is quite close to the range of 0.4to 0.6 obtained for SCI,B/SUC,B. The highest variability of ± 0.12 forB,UCB,CI,A,A/SSSS is obtained for k=0.8. For the remaining k values the variability ofB,UCB,CI,A,A/SSSS can be expressed within ± 0.05. This finding is very similar to the finding obtained for the variability of SCI,B/SUC,B.

Fatigue Crack Initiation Potential from Defects in terms of Local Stress Analysis

The competition of surface and subsurface crack initiation induced failure is critical to understand very high cycle fatigue（VHCF） behavior, which necessitates the elucidation of the underlying mechanisms for the transition of crack initiation from surface to interior defects. Crack initiation potential in materials containing defects is investigated numerically by focusing on defect types, size, shape, location, and residual stress influences. Results show that the crack initiation potency is higher in case of serious property mismatching between matrix and defects, and higher strength materials are more sensitive to soft inclusions（elastic modulus lower than the matrix）. The stress localization around inclusions are correlated to interior crack initiation mechanisms in the VHCF regime such as inclusion-matrix debonding at soft inclusions and inclusion-cracking for hard inclusions（elastic modulus higher than the matrix）. It is easier to emanate cracks from the subsurface pores with the depth 0.7 times as large as their diameter. There exists an inclusion size independent region for crack incubation, outside which crack initiation will transfer from the subsurface soft inclusion to the interior larger one. As for elliptical inclusions, reducing the short-axis length can decrease the crack nucleation potential and promote the interior crack formation, whereas the long-axis length controls the site of peak stress concentration. The compressive residual stress at surface is helpful to shift crack initiation from surface to interior inclusions. Some relaxation of residual stress can not change the inherent crack initiation from interior inclusions in the VHCF regime. The work reveals the crack initiation potential and the transition among various defects under the influences of both intrinsic and extrinsic factors in the VHCF regime, and is helpful to understand the failure mechanism of materials containing defects under long-term cyclic loadings.

STUDY ON FATIGUE SHORT CRACK GROWTH LAW AND FATIGUE LIFE FOR MEDIUM CARBON STEELS

The fatigue crack initiation from notch root and the short-crack growth laws of two medium carbon alloying structural steels—35CrMo and 42CrMo are investigated under the different stress ratios R =0.1, 0.3) and three-point bending condition. The relationships between the maximum stress range at the notch root Δ σ max and the number of cycles before fatigue crack initiation N i are determined. The threshold stresses of fatigue crack initiation (Δ σ max ) th are got, and the smallcrack growth laws are obtained for these steels. An effective and convenient method is proposed for predicting the fatigue life of the notch specimens.

Crack initiation of granite under uniaxial compression tests:A comparison study

In this study,a combination of acoustic emission(AE)method(AEM)and wave transmission method(WTM)is used to investigate the behaviors of AE and ultrasonic properties corresponding to initial fracturing in granitic rocks.The relationships of AE characteristics,frequency spectra,and spatial locations with crack initiation(CI)are studied.The anisotropic ultrasonic characteristics,velocity distributions in different ray paths,wave amplitudes,and spectral characters of transmitted waves are investigated.To identify CI stress,damage initiations characterized by strain-based method(SBM),AEM and WTM are compared.For granite samples,it shows that the ratio of CI stress to peak strength estimated by SBM ranges from 0.4 to 0.55,and 0.49-0.6 by WTM,which are higher than that of AEM(0.38-0.46).The CI stress identified by AEM indicates the onset of microcracking,and the combination of AEM and WTM provides an insight into the detection of rock damage initiation and anisotropy.

GROWTH OF SHORT CRACKS OF A537CLI STEEL UNDER FATIGUE LOADING IN 3.5% NaCl SOLUTION

The effects of environmental media,both in atmosphere and in 3.5% NaCl aqueous solution, on the growth of short cracks in comparison with the long ones have been investigated under fatigue loading on the specimens of single-edge crack about 0.05—0.15 mm for A537CLI steel.The growth rate of short cracks is faster than those of long ones around the threshoht stress intensity.The threshold stress intensity for short crack growth decreases with de- creasing crack length.The acceleration effect of the salt water,as compared with atmosphere environment,on the growth of short cracks under fatigue is much greater than that on the growth of long cracks.

Crack Initiation under Cyclic Compression

The crack initiation behaviour under cyclic compression foy the notched specimen was investigated. It has been found that the cycles for crack initiation increase with the increase of compressive mean stress, and the decrease of stress amplitude. The stress amplitude plays a more important role than the mean stress does. Photoelastic coating and finite element methods were employed to measure and calculate the stress field in the notched part. The resul ts show that the crack initiation under compression is attributed to the tensile stress which may exist during unloadtng. If the true stress state in the notch is compressive, no crack initiates.

Theoretical Analysis and Experimental Verification of Crack Initiation Characteristics of Compression-Shear Plane Crack with Hydraulic Pressure

In this paper, the crack initiation characteristics of compression-shear plane crack with hydraulic pressure were studied by using theoretical analysis and experimental verification methods. The formula derivation process of stress intensity factor of crack tip and open-type crack initiation angle and initiation strength was expounded in detail. Cement mortar specimens prefabricated with open-type crack were made for biaxial compression test. The results show that the mode I stress intensity factor is inversely proportional to the dip angle of pre-exciting crack, water pressure and crack width. The fracture toughness is most easily achieved when the dip angle of pre-exciting crack is 60°. The mode II stress intensity factor is symmetrically distributed with the dip angle and independent of the water pressure and crack width. For open-type crack, the crack initiation angle decreases with the increase of the dip angle of pre-exciting crack, water pressure and crack width;the crack initiation strength is inversely proportional to the water pressure and proportional to the lateral pressure. The research results can provide ideas for the study of crack initiation under the coupling of ground stress and osmotic pressure in tunnel engineering.

Experimental investigation of stress unloading effects on rock damage and confining pressure-dependent crack initiation stress of porous sandstone under true triaxial stress environments

This study investigates the impact of intermediate(σ_(2))and minimum(σ_(3))principal stress unloading on damage behavior and the confining pressure influence on crack initiation stress(σci)in true triaxial stress conditions,utilizing large-scale cubic samples.Two distinct true triaxial tests were executed,examining the effects of confining stress(σ_(2)andσ_(3))unloading on porous sandstone damage and the correlation between confining stress andσci.Acoustic emission(AE)parameters,signal characteristics,and wave velocity variations were utilized to elucidate cracking mechanisms and damage development in the samples.Unloading tests reveal consistent ve-locities in three orthogonal directions(V_(11),V_(22),and V_(33))during the initial two unloading stages.In the subse-quent three stages,confining stress unloading leads to a decrease in wave velocity in the corresponding direction,while velocities in the other two directions remain nearly constant.Notably,σ_(2)unloading generates higher amplitude AE signals compared toσ_(3)unloading,with over 70%of the micro-cracks categorized as tensile.In the incremental loading tests,σ_(ci) is found to be contingent on confining pressure,withσ_(2)playing a crucial role.Duringσ_(1) loading,V_(33) decreases,indicating additional crack formation;conversely,σ_(3)loading results in V33 increase,signifying the continuous closure of existing cracks.Limitations of the experiments are summarized and prospects in this domain are outlined.

A Statistical Study on the Initiation and Growth Lives of Short Fatigue Cracks

In order to clarify the physical background of the scatter in fatigue behaviour, rotary bending fatigue tests are carried out using smooth speciments of a medium carbon steel with two kinds of grain sizes. The statistical characteristics of short carck initiation and growth lives are investigated by a new definition of short fatigue crack initiation. Detailed analysis reveals that the distribution of short crack initiation life can be expressed by two or threeparameter Weibull distribution, and the threeparameter Weibull distribution is well fitted to the distribution of short crack growth life, and the grain size and stress level have a great influence on the statistical characteristics of crack initiation and growth life.

Microstructure features induced by fatigue crack initiation up to very-high-cycle regime for an additively manufactured aluminium alloy

Fatigue failure can still occur beyond 107 cycles,i.e.very-high-cycle fatigue(VHCF),in many metallic materials,such as aluminium alloys and high-strength steels.For VHCF of high-strength steels,a fine granular area(FGA)surrounding an inclusion is commonly identified as the characteristic region of crack initiation on the fracture surface.However,no such FGA feature and related crack initiation behaviour were observed in VHCF of conventionally cast or wrought aluminium alloys.Here,we first reported the distinct mechanisms of crack initiation and early growth,namely the microstructure feature and the role of FGA in VHCF performance for an additively manufactured(AM)AlSi10Mg alloy.The AM pores play a key role in fatigue crack initiation similar to that of the inclusions in high-strength steels,resulting in almost identical FGA behaviour for different materials under a range of mean stress with a stress ratio at R<0 or R>0.The profile microstructure of FGA is identified as a nanograin layer with Si rearrangement and grain boundary transition.This process consumes a large amount of cyclic plastic energy making FGA undertake a vast majority of VHCF life.These results will deepen the understanding of VHCF nature and shed light on crack initiation mechanism of other aluminium and AM alloys.

Effects of stick-slip on stress intensity factors for subsurface short cracks in rolling contact

This paper theoretically investigates the effects of stick-slip in roiling contact zone on stress intensity factors （SIFs） for sub- surface short cracks. New mathematical models for SIFs including stick-slip ratio are deduced in two cases. One is a subsur- face short crack parallel to surface, and the numerical analysis shows that the value of Kn increases with the increase of stick-slip ratio; the other is a subsurface short crack perpendicular to the surface, and the numerical analysis indicates that the positive value of KI decreases with the increase of stick-slip ratio. As AKI and AKI are necessary to evaluate the fa- tigue crack propagation rate or fatigue lifetime, the influences of stick-slip ratio on them are then discussed. It is found that the maximum variations of AK1 and AKu are both around 3.0% due to stick-slip ratio variation.

Theoretical study on Manson-Coffin equation for physically short cracks and lifetime prediction

The Manson-Coffin equation has been widely applied to the prediction of fatigue lifetime.But this equation does not explicitly express the relation between the fatigue lifetime and the crack length.The present paper proposes that the grain size can be re-placed by the maximum non-damaging crack length.Thus,the growth rate will decrease to zero when the crack reaches this size.Combining with the theory of the fatigue short crack propagation,we derived the relations between physically short crack's initiation-propagation rates and material's mechanical properties,as well as crack length,stress and strain.With the derived relations,fatigue lifetime of short cracks can be successfully predicted by basic mechanical properties.Similar to the format of Manson-Coffin equation,our relations uncover the essence of Manson-Coffin equation which may reveal the short crack's initiation-propagation mechanism.Predictions of fatigue lifetime using our relations were compared with the results of well-known experiments.Good agreement is found in many aspects,such as coefficients,exponents,as well as fatigue life-times,especially for short cracks around 10 micrometers.Predictions on the short crack propagation rates are also compared for 16 types of carbon steels.Satisfactory consistency shows that our relations have wide applicability.

Influence of Rare Earth Element on Short Fatigue Crack Threshold for Al－Li Alloy 2090

Curves of △Kth vs.△ath and △Kcl·th vs.△ath for aluminum-lithium alloy 2090 have been determined and compared with those for traditional aluminum alloy 2024.The growth resistance of short fatigue cracks for aluminum-lithium alloy 2090 is quantitatively evaluated.The essential reason resulting in stronger short cracks effect has been ascertained.Influence of cerium on the growth behavior of short fatigue cracks for aluminum-lithium alloy 2090 was investigated.The results show that by adding cerium into this alloy a significant improvement in △Ki can be achieved and at the same time △Kcl·th is increased.Consequently,the essential factor resulting in lower growth resistance of short fatigue cracks for this alloy is removed and the growth resistance of long and short fatigue cracks is increased.

SHORT FATIGUE CRACK BEHAVIOUR IN ISO-STRESS SPECIMENS

Fatigue tests were made on a vibration machine using specially designed specimens to investi- gate the initiation and propagation features of short fatigue cracks in a weld metal.The spec- imens were triangular in shape so that when loaded as a cantilever beam the surface tensile stress is constant.Test results show that short fatigue cracks mainly originate from slip bands within ferrite grains.The development of short fatigue cracks is marked by a gradual increase in crack density with fatigue cycles.Coalescence of short cracks leads to crack propagation and the crack path is predominantly transgranular.

A STATISTICAL INVESTIGATION OF THE BEHAVIOR OF SHORT FATIGUE CRACK IN MEDIUM CARBON STEELS

Rotary bending fatigue tests were carried out by using smoothspecimens of medium car- bon steel with two ferrite grain sizes. Inorder to clarify the physical background of the scatter in fa- tiguebehavior, the statistical characteristics of the initiation andgrowth of short fatigue crack were in- vestigated. Results show thatthe short crack initiation and growth life distribution can beexpressed by two-or three-parameter Weibull distribution. The Weibulldistribution of the mixed type is well fitted to the crack lengthdistribution for both steels. The knee values of Weibull plots arerelated to the grain size.

Influence of Stress Ratio and Loading Condition on Near-threshold Fatigue Crack Growth Behaviour

Near-threshold fatigue crack propagation behaviour of a cold-worked copper tested with distinct fa- tigue testing systems under different stress ratios has been investigated.The emphasis was placed on the evaluation of crack closure effect as well as the effective fatigue threshold,It was found that the fatigue threshold for R=0 is higher than those for R=-1 and R=0.4,for which almost the same threshold value was derived.Compared with the conventional closure evaluation method,the pro- posed new closure evaluation method can generally interpret the dependence of the fatigue thresh- old on stress ratio and loading condition,and leads to a higher and relatively constant effective fa- tigue threshold of about 3 MPa·m^(1/2) for the cold-worked copper at different stress ratios and loading conditions.

THRESHOLD OF SHORT FATIGUE CRACK FOR Al-Li ALLOY 8090

Threshold of fatigue for short through cracks for Al-Li alloy 8090 was evaluated to be lower than that of long cracks,and to decrease with the shortening of the crack length.The correla- tion among the threshold,crack wake,and crack tip shielding of the short fatigue cracks was discussed.The super demarcation length and lowest theoretical threshold of short through fa- tigue cracks were presented.

Interacting mechanism and initiation prediction of multiple cracks

The maximum Mode Ⅰ and Mode Ⅱ stress intensity factors(SIFs), KI,kmax(θ) and KII,kmax(θ)(0°<θ<360°), of inclined parallel multi-crack varying with relative positions(including horizontal and vertical spacings) are calculated by the complex function and integration method to analyze their interacting mechanism and determine the strengthening and weakening zone of SIFs. The multi-crack initiation criterion is established based on the ratio of maximum tension-shear SIF to predict crack initiation angle, load, and mechanism. The results show that multi-crack always initiates in Mode Ⅰ and the vertical spacing is better not to be times of half crack-length for crack-arrest, which is in good agreement with test results of the red-sandstone cube specimens with three parallel cracks under uniaxial compression. This can prove the validity of the multi-crack initiation criterion.

Controlling of weld hot cracks of aluminum alloy sheets by transverse pre-stressing

A new ideological and theoretical model—a technology to control weld hot cracks by transverse compressive pre-stress in the welding of aluminum alloy was put forward,which was further proved by the subsequent self-designed test setup.Experiments are conducted on the fishbone shaped specimen under conventional welding and welding with various pre-stress values.The experimental results turn out that,the initiation rate of the weld hot cracks decreases with increasing values of the compressive pre-stress.When the pre-stress reaches 0.3-0.4 of the yield stress,the cracks even disappear.In mechanical viewpoint,the researches here develop a new way to control weld cracks.