Negative Load Ratios Research Articles

A digital twin approach toward unlocking elasto-plastic fatigue crack growth rates under negative load ratios

This paper introduces a novel digital twin solution for unlocking the elasto-plastic fatigue crack growth within an S550 steel under negative load ratios. The digital twin transforms solely strain data from a strain-interfaced welded plate joint specimen to the load–displacement curve to compute cyclic J-integral values using the η approach, eliminating the need for load and displacement measurements. The accurate computation of the elasto-plastic ΔJ effectively extends the fatigue crack growth relationship derived from standard fracture specimens. The extended fatigue crack growth relationship accurately predicts the fatigue life of specimens under separate step-up and step-down variable amplitude loading regimes.

Cyclic creep strain rate criterion for short-fibre reinforced thermoplastics: Validation of creep and fatigue performance across a wide range of load ratios

The fatigue and creep responses of short-fibre reinforced thermoplastic matrix composites are influenced by numerous parameters such as load ratio for fatigue. Fatigue criteria, based solely on the evolution of the cyclic creep of the mean strain, are effective for load ratios greater than zero (tension/tension) but have limitations for negative load ratios (tension/compression).The aim of this study was to propose a unified creep and fatigue criterion, based on the evolution of the cyclic creep of the maximum strain, that allowed both load ratio domains to be covered. To investigate a wide range of load ratios (-1 to 0.8), an existing creep and fatigue database was augmented with purely alternated tension/compression tests. This database, which included 489 tests, considered the variations in parameters that influence the creep and fatigue responses, such as fibre orientation, water content and specifically for fatigue load ratio and frequency. This was used to validate a unified criterion based on the cyclic creep of the maximum strain. This criterion improved fatigue life prediction compared to existing criteria and allowed fatigue and creep results to be unified with 87% of estimated lifetimes within a scatter band of factor two.

Fatigue crack growth under mixed mode I-II loading with a single tensile overload at negative load ratios

Fatigue crack growth (FCG) behavior under mixed mode loading has been received extensive attention, including overload condition. The mixed mode I-II fatigue crack growth behavior of commercial pure titanium (CP-Ti) with tensile overload at negative load ratios was investigated by experiment and finite element method (FEM). The effects of loading angle, load ratio and overload on mixed mode I-II fatigue crack growth were discussed with a modified compact-tensile-shear (CTS) specimen. The mechanism of mixed mode crack growth with overload was revealed. Fatigue crack growth path and fatigue crack growth rate (FCGR) with/without overload were compared experimentally, and overload retardation effect was investigated. The variation of plastic zone and the distribution of stress and strain were simulated through finite element method. The mechanism of overload retardation effect of mixed mode I-II crack growth under compressive load was illustrated by microscopic perspective, crack closure and residual compressive stress at crack tip, and the weakening effect of mode II shear component and compressive load effect on overload retardation effect was demonstrated.

Predicting fatigue damage in composites subjected to general loading conditions

A computationally efficient fatigue analysis methodology is proposed that uses a cycle jump approach to drive the accumulation of fatigue damage and a unified local fatigue cohesive zone model that can predict the initiation and propagation of cracks using a reduced set of model parameters. A new definition of the stress ratio is proposed for general loading conditions, which include negative load ratios, unsynchronized loads, and problems where the mode mixity changes during a cycle. The cycle jump procedure was verified by performing analyses of standard double cantilever beam and mixed mode bending tests. Then, the model was validated by performing analyses of double notch shear tests and initiation of transverse matrix cracking in a [0/90] laminate using models that account for residual thermal stresses. The results indicate that the analysis methodology can reproduce experimentally measured fatigue damage initiation and evolution for a variety of different configurations and load combinations.(Keywords: C. Cohesive interface modelling, B Fatigue, B. Delamination, A. Polymer-matrix composites (PMCs))

Effect of single tensile overload on fatigue crack growth behavior of CP-Ti at negative load ratio

In present study, the fatigue crack growth (FCG) behavior of commercial pure titanium (CP-Ti) at negative load ratio with a single tensile overload was investigated through the combination of experiment and finite element method (FEM). The influence of load ratio and overload ratio was considered to investigate the overload retardation effect of FCG with compact-tensile-shear (CTS) specimens. Changes of the fatigue crack growth rate (FCGR) and crack opening force before and after overload were obtained experimentally under different loading conditions. The mechanical behaviors of stress–strain distribution and evolution of plastic zone size ahead of crack tip were explored by FEM for revealing the mechanism of overload at negative load ratios. The results demonstrate that retardation effect of FCG increases with overload ratio, and decreases with load ratio. The retardation effect of overload occurs after a transient acceleration of FCGR. The excessive residual compressive stress induced within the unloading stage of overload cycle ahead of crack tip, causes a shielding effect, which is one of the main factors of overload retardation effect. The difference of plastic strain at crack tip before and after overload makes the monotonic plastic zone (MPZ) and reverse plastic zone (RPZ) compete with each other, resulting in an increase of residual plastic strain, which hinders the crack propagation. At negative load ratios, the overload retardation effect will be weakened by the compressive load because of the decreasing residual plastic strain.

Numerical investigation of mechanical behavior of crack tip under mode I and mixed-mode I-II fatigue loading at negative load ratios

The mechanical behavior of crack tip under mode I and mixed-mode I-II fatigue loading for commercial pure titanium at negative load ratios are carried out by finite element method in this paper. The effects of maximum fatigue load, load ratio, loading angle and normalized crack length on the mechanical behavior of crack tip are discussed. The change of mechanical behavior of crack tip is analyzed through the evolution of strain energy. The results show that the increase of maximum fatigue load and crack length increase the plastic strain accumulation at crack tip in mode I fatigue crack growth (FCG), which causes the crack tip release more fracture energy to drive crack growth and affect the distribution of stress-strain field. The decrease of load ratio also increases the plastic strain accumulation and the plastic energy dissipation at crack tip. In mixed-mode I-II FCG, the larger loading angle increase the resistance of crack deflection and cause more plastic strain accumulation at crack tip. After the crack deflects, the crack growth increases the crack tip plastic zone and the morphology of plastic zone changes continuously, which cause the crack growth path move away from the mode I crack growth direction. Different loading angles produce different crack growth paths, which deviates from mode I crack growth direction with the increase of loading angle.

Experimental and numerical investigation on fatigue crack growth behavior of commercial pure titanium under I-II mixed mode loading at negative load ratios

With the increase of design and application parameters for pressurized structures, the mixed mode fatigue crack growth (FCG) behavior has become a concerned problem in the field of structural integrity. In order to understand FCG behavior of I-II mixed mode crack growth at negative load ratios, an improved compact tensile shear (CTS) specimen of commercial pure titanium is taken to study the effects of load ratio and loading angle on I-II mixed mode FCG behavior through experiments and finite element method (FEM), which mechanism is discussed in depth as well. The contribution of mode I and mode II crack growth driving forces to I-II mixed mode FCG is analyzed. The changes of crack fracture criterion and the mechanism of crack growth in I-II mixed mode FCG process are revealed, and the competition relationship between two crack closure mechanisms of I-II mixed mode crack at negative load ratios is explained. An improved fatigue crack growth rate (FCGR) model that can make I-II mixed mode FCGR normalized is proposed by considering both the crack closure and the crack fracture criterion eventually.

Effect of compressive load and crack closure on fatigue crack growth of commercial pure titanium at negative load ratios

In this paper, the effect of compressive load and crack closure on mode-I fatigue crack growth (FCG) behavior at negative load ratios is studied with compact-tensile-shear (CTS) specimens made from commercial pure titanium (CP-Ti). The FCG behavior at negative load ratios under constant maximum load controlled has been explained by the interaction of compressive load effect and crack closure. The variation of crack closure level at negative load ratios within stable crack growth stage is obtained by the experiment. The crack closure level keeps constant which makes the crack closure effect dominate the FCG behavior in pre-stage. While in post-stage, the crack closure level drops gradually. The crack closure effect can be neglected currently and the compressive load effect plays a dominate role in post-stage. Meanwhile, the influence of crack closure effect on mechanical behavior at crack tip is described by finite element method (FEM) to explain the anomaly in pre-stage. It is confirmed that there exists a maximum reversed plastic zone induced by the crack closure effect during unloading process in pre-stage at negative load ratios.

Two new models of fatigue crack growth rate based on driving force parameter and crack closure method at negative load ratios

The fatigue crack growth rate (FCGR) is strongly dependent on the load ratio R and most FCGR models are established on the basis of R. At present, there are more FCGR models with positive load ratio. In this paper, fatigue crack growth (FCG) behavior of commercial pure titanium at negative load ratios is studied. The FCGRs at various load ratios are fitted by driving force parameter model and crack closure model. The advantages and disadvantages of different models are analyzed by calculating the dispersion of FCGR curves which are condensed by each model. Improved two-parameter driving force model and proposed crack closure model are proposed by two FCGR modeling methods, respectively. One is to modify the FCGR by improving the stress intensity factor (SIF) K with the two-parameter driving force method. Another is established by correlating the crack closure ratio U and load ratio R, positive SIF range ΔK+, maximum SIF Kmax based on the variation of crack closure level in stable crack growth stage. It is found that proposed crack closure model is superior to the former in both the condensation effect and the physical significance. Under different loading conditions, proposed crack closure model can reliably and accurately condense the FCGR curves and reflect the variation of crack closure level in the whole stable crack growth stage. The integrity and validity of proposed crack closure model is also further verified by FCGR data of other researchers.

Fracture resistance curve for single edge notched tension specimens under low cycle actions

This paper investigates monotonic and cyclic fracture behaviors of aluminum alloy 6061-T6511 and analyzes the cause of different fracture behaviors. This study adopts the η approach and a modified η approach to obtain monotonic and cyclic J-R curves respectively. The cyclic loaded SE(T) specimens with zero load ratio have similar J-R curves with monotonically load SE(T). In contrast, a tensile residual stress field at the crack front introduced by negative load ratios promotes a faster crack extension, which leads to a lower load resistance at the same CMOD level. The strain energy corresponding to the area under the P-CMOD envelope becomes lower, which induces the degradation of cyclic J-R curve with negative load ratios.

Applications of fracture mechanics in assessing integrity of hydrogen storage systems

This paper addresses the challenges in designing high pressure, durable, safe, and cost-effective vessels for storage of gaseous hydrogen and the role of fracture mechanics in meeting those challenges. The design life limiting material property for vessels made from tempered martensitic steel is the environment assisted fatigue crack growth rate (FCGR) that depends on ΔK, the load ratio, loading frequency, and the H2 pressure. The effects of these variables individually and synergistically are explored in this paper. FCGR behavior at negative load ratios, R, of −1.0 and −0.5 were found to be comparable to those at load ratios of 0.1 and 0.2; the effects of load ratio appear to become stronger for R > 0.2. The effect of decreasing loading frequency, ν, on the FCGR behavior in H2 gaseous environment is small for frequencies less than 1 Hz. FCGR behavior is shown to increase with gas pressure and the effect appeared to be highest in going from air environment to 10 MPa H2 pressure and then it saturated at 45 MPa. The impact of these variables and others such as autofrettage, on the design life of H2 storage vessels are explored.

Fatigue Crack Growth in an Al-Mg-Si Alloy under Negative Load Ratio

The usual approaches for Fatigue Crack Growth (FCG) assessment are based on semi-empirical models that consider the stress intensity factor range of fracture mechanics, ΔK, as the governing driving force for crack propagation. However, FCG data incorporating compressive loads have brought discussions and controversies. The compressive loads are not taken into account in the usual life prediction codes and the negative portion of the loading cycle is neglected. In the present work, constant amplitude fatigue crack growth tests with load ratios-1 and 0 are performed, for two diferent stess levels, in AA 6005 alloy centre-notched middle tension M(T) specimens and the obtained results are discussed. It is shown that the crack closure concept, that usually work well for positive ratios, is not enough to satisfactorily explain the negative load ratio effects. The results also showed how the negative part of the load affected the propagation rate of the crack, mainly for larger cracks and smaller loads. Finally, it is shown that a previously proposed expression for the stress distribution ahead of the crack can shed some light on this question.

On single-edge-crack tension specimens for tension-compression fatigue crack growth testing

Single-edge-crack (SEC) specimens with rigid threaded ends are well suited for fatigue crack growth testing in extreme environments and for conducting tests at negative load ratios. Stress intensity parameter, K, and crack mouth opening displacement, CMOD, solutions as a function of crack size for this geometry are derived using 3-D finite element analyses using multiple codes. Both K and CMOD values obtained are shown to be comparable between the various finite element codes used. The solutions are sensitive to the height (2H) to width (W) ratio of the specimen, as well as to the aggregate bending stiffness of the members of the loading train. A procedure utilizing the computational results for various 2H/W values and a set of specially designed fatigue crack growth experiments is described to develop custom solutions for estimating K and CMOD values that account for both, the 2H/W ratio and the bending stiffness of the loading train.

Compressive Overload Effects on the Resonance Frequency of Monocrystalline Silicon Microbeams and Implications for Fatigue Mechanisms

Previous work demonstrated the marked effect of load ratio on the fatigue life of both mono- and poly-crystalline silicon thin films, with decreasing fatigue lives for more negative load ratios. In this paper, we investigated the role of a single compressive load on the stiffness (and therefore flaw population) of a monocrystalline Si microbeam. Specifically, we measured the resonance frequency (f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ~ 40 kHz) of a microresonator with ppm-level resolution before and after applying a compressive stress ranging from 1.5 to 5.5 GPa. The resolution in J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> measurements is enough to capture the formation of subcritical penny-shaped cracks (lateral dimensions tens of nanometers), or the extension of existing cracks. No significant decrease in f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> was measured within the resolution of the technique. This result indicates that the mechanism known for the fatigue of notched ceramics under cyclic compressive loads at the bulk scale, relying on the formation of cracks upon the first compressive cycle, does not apply to the fatigue of silicon thin films. Instead of a decrease in J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , the results highlighted an increase in J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> in some specimens, which is interpreted as compression-induced crack healing (as opposed to the well documented thermally induced healing). A review of the proposed fatigue mechanisms for Si thin films is also provided.

Study of Fatigue Crack Growth in Al-Mg-Si Alloys Using a Predictive Model under Positive and Negative Load Ratios

The study of fatigue crack growth (FCG) is aimed at residual life estimations in order to apply the damage tolerant criterion. Usual approaches are based on semi-empirical models that consider the stress intensity factor range of fracture mechanics, ΔK, as the governing driving force for crack propagation. An alternative approach is the use of predictive theoretical schemes arising from damage mechanics. Although they havent achieved a reliability level high enough to be used in design, predictive models may be important in some situations like material selection. In the present work, a predictive FCG method based on the cumulative damage of volume elements along the crack path is employed. The development of the work includes considerations about the stress distribution in the cracked body and the stress-life and strain-life relations used in the computational procedure. A previously developed analytical expression for the stress distribution ahead of the crack in a finite width plate, based on the numerical analysis performed by the Finite Element Method, is used in the predictive method. The stress field is determined for both upper and lower limits of cyclic loadings. The fatigue crack growth behavior of three Al-Mg-Si alloys: AA 6005, AA 6351 and AA 6063, tempered and aged for the T6 condition, was analysed for positive and negative R-ratios. In order to check the model results, constant amplitude FCG tests with load ratios ±0,5 were carried out in M(T) specimens. The experimental results, compared to the computational simulations, show that it is possible to obtain predictions of FCG behaviour for both positive and negative load ratios.

Crack growth characterisation of A356-T7 aluminum alloy under thermo-mechanical fatigue loading

This paper presents results and interpretations of several long crack thermo-mechanical fatigue tests on A356-T7 cast aluminum alloy used in automotive cylinder heads. These tests were conducted on CT16 and SEN specimens for different positive and negative load ratios, temperatures, frequencies and stress intensity factor values in order to establish the contribution of each parameter governing the fatigue crack propagation. It was shown that the decrease of the frequency causes significant increase of the crack growth rate especially at high temperatures and load ratios. The performing of negative load ratio tests had shown a primordial importance of the compressive load part of fatigue on the crack advance. In addition, SEM, optical microscopy and other metallographic techniques were used to examine fracture surfaces and to analyze particles cracking. For positive load ratios tests, it was shown that in stage II (Paris regime) and stage III (high crack growth rates) the number of cracked particles increases with Kmax and gradual changes in fracture surface appearance occur. These changes were associated with different crack growth mechanisms at the microstructural scale. The amplitude of the inelastic deformations and the extent of the plastic zone ahead of the crack tip were used to explain the observed changes in crack growth mechanisms. The crack growth under negative load ratio loads is especially analyzed, and a way of deriving this rate is given and shown to be relevant even for nonisothermal loading.

OS1301 マグネシウム合金押出材の過渡的き裂進展挙動に及ぼす応力比変動の影響 : 第2報 試験片切出し方向の影響(OS13-1 応力特異場の解析と材料強度-1,OS-13 応力特異場の解析と材料強度)

Fatigue tests were carried out using extruded Mg alloy AZ31 to study effect of negative load ratio on crack propagation behavior. In the tests, R ratio was changed into the negative value. When the minimum stress exceeds over the value of the compressive yield strength of the material, the rate of crack propagation accelerated suddenly due to occurrence of the twinning.

Monitoring fatigue damage growth in polysilicon microstructures under different loading conditions

Nucleation and accumulation of damage in polysilicon microstructures under fatigue loading cycles are investigated with respect to the maximum applied stress. Measurements are performed with negative load ratios on a 15 μm thick notched MEMS specimen, with a notch radius of 0.5 μm. The damage in the material is investigated by means of an elastic stiffness decrease monitoring during fatigue life, obtained through a low noise, low perturbing capacitive position readout of the MEMS moving mass. The system is capable to detect elastic stiffness changes with a resolution <20 ppm/Hz 1/2. Experimental results show the existence of different damage accumulation dynamics, with respect to the maximum applied stress: beneath a lower stress limit, damage accumulation is not observed (within the system resolution) up to 2 × 10 9 cycles; above an upper stress limit, the delayed device failure happens suddenly (it is not anticipated by any detectable stiffness decrease) after ∼10 5 cycles; between these conditions, a slow, stable damage growth is evidenced through the analysis of the stress dependent stiffness decrease prior to the device failure, which happens after more than 10 6 to 10 7 cycles. It is thus suggested the presence of two distinct damaging phenomena, which both lead to the device delayed rupture but with different temporal dynamics.

510 マグネシウム合金のき裂進展特性に及ぼす負の応力比の影響(GS8-2 材料力学)

510 マグネシウム合金のき裂進展特性に及ぼす負の応力比の影響(GS8-2 材料力学)

1102 マグネシウム合金押出材のき裂進展並びにき裂閉口挙動に及ぼす正から負への応力比変動の影響(OS11-1 材料の疲労挙動と損傷評価-き裂進展-)

Fatigue tests were carried out using extruded Mg alloy AZ31 to study effect of negative load ratio on crack propagation behavior. In the tests, R ratio was changed into the negative value. When the minimum stress exceeds over the value of the compressive yield strength of the material, the rate of crack propagation accelerated suddenly due to occurrence of the twinning.