Critical Damage Value Research Articles

Strain performance and fracture response characteristics of hard rock under cyclic disturbance loading

Fracture characteristics and damage mechanism of rock mass under cyclic loading and unloading is one of the basic research topics of rock mechanics. To study the deformation and fracture response characteristics of brittle hard rock under cyclic disturbance loading, cyclic loading and unloading tests were carried out at different loading and unloading rates, and the stress-strain curve shapes, modulus elastic, critical damage value, fracture characteristics and fractal dimension laws were analyzed. The results show that the loading and unloading effect has significant influence on stress-strain curve shape and fatigue life. The hysteresis loop is overdistributed from sparse to dense with increasing loading and unloading rate and fatigue life is significantly reduced. The loading and unloading action has a phased control effect on peak strength with a first increases and then decreases. The rock has a stable rupture type with a brittle strength about 1.16~31.07% of peak strength, and brittle strength indicates a brittle fracture. With increasing cycle number, loading elastic modulus and unloading elastic modulus firstly increase sharply then increase linearly and finally decrease gradually. The critical damage factor has an approximately linear relationship with loading and unloading rates. The rock mainly occurs oblique shear through and tension through ruptures, and the failure types changes from shear failure to tension failure excessively with increasing loading and unloading rate. The increased loading and unloading rate weakens the end constraint effect, the greater the loading and unloading rate, the more obvious the fragmentation degree, and the more significant the fragments uniformity. The fractal dimension is logarithmic function related to loading and unloading rate.

Effect of Inclusions on Internal Fracture in Skew Rolling

This paper discusses the effect of inclusions on internal fracture in skew rolling. The prediction of internal fractures is crucial given that internal fractures cause loss of product strength and are difficult to detect. Our previous report, published in 2019, proposed a new ductile fracture criterion that considers the effect of shear stress on void coalescence in a cylindrical coordinate system. This paper covers the following three points: (1) the evaluation of the hot workability of materials with different inclusions in tensile testing, (2) the relationship between the hot workability and the damage value determined using the proposed criterion, and (3) the effect of inclusions on void evolution in skew rolling. Given that the critical damage value decreased with decreasing hot workability, internal fractures are more likely to occur in a material that contains numerous large inclusions. The experimental results led to the hypotheses that the plastic strain nucleates the voids originating from inclusions and that shear stress allows the voids to coalesce. This study has demonstrated that decreasing the diameter and number density of inclusions is effective toward suppressing internal fractures.

Investigation on the modelling and characterization of top edge burr formation in slotting finned tube

In this study, a three-dimensional finite element model is utilized to analyse the top edge burr formation in orthogonal slotting copper finned tubes. To describe the top edge burr generation, a conceptual model is developed to explain the material shear failure. The normalized Cockroft-Latham criterion is employed for a general understanding of the plastic behaviour and burr formation, and the critical damage value is obtained to qualify the burr geometries by tensile tests. Based on material side flow and the progressive deformation behaviour, the characteristics and mechanism of top edge burr formation are further investigated. The results show that the top edge burr is formed by a combination of material tear and sideward flow. The top edge burr formation process can generally be divided into three phases: the initiation of the deformation bulge, the development of the deformation bulge, and tear formation. The characteristics of the top edge burr also consist of three parts: basal deformation area, tensile area, and top tear area. The three parts of the burr characteristics correspond to the three phases of the burr formation process. Additionally, the influences of rake face, feed rate, and cutting speed on the burr size are studied based on a quantitative method. The study provides a basis for the minimization of top edge burr formation and optimization of machining parameters.

Rubber–fibre composite modelling and its influence on fatigue damage assessment

AbstractA novel multiaxial energy‐based approach is presented and used to demonstrate the influence of different finite element (FE) modelling techniques on the prediction of the fatigue life of a rubber composite with long oriented fibres. It is shown that the simplest modelling methods using 2‐D elements with rebar layers, layered 2‐D elements or layered 3‐D elements do not allow for a precise determination of the critical location and damage value. In contrast, modelling methods with 3‐D matrix and discrete reinforcement provide much better results. The predicted critical location corresponds to the measured one, although the predicted fatigue life still differs from the measured results. The most complex microscopic modelling method shows the best agreement between the predicted and measured fatigue life. Because microscopic modelling is not suitable for modelling larger products made of rubber–fibre composite, it is also noted that modelling techniques with 3‐D matrix and discrete reinforcing elements can be used with the same accuracy if the fatigue life curve is obtained from measurements on the specimens made of composite material rather than the specimens made of the critical base material (rubber).

Meso-Damage Mechanism of Strength and Deformation Characteristics of Typical Sandstone in Xinwen Coalfield

Geotechnical engineering problems will cause asymmetric deformation of surrounding rock, which is not conducive to the stability of rock mass. In order to study the meso-damage mechanism of rock strength and deformation characteristics, taking three kinds of typical sandstone as examples, the meso structure images of sandstone were obtained by JSM-6510LV scanning electron microscope (SEM). According to the meso-structure images and fractal theory, MATLAB was compiled to calculate the fractal dimension of the meso-structure images of the three types of sandstone. The uniaxial compression test of sandstone is carried out by using the Shimadzu electronic universal testing machine. The mechanical parameters of three types of sandstone are obtained. By comparing the relationship between fractal dimension and mechanical parameters, the correlation between strength and deformation characteristics of sandstone and mesostructure is analyzed. The results show that sandstone has the characteristic of self-similarity. The fractal dimension of sandstone decreases with the increase in magnification. The macro-mechanical properties of sandstone are closely related to the meso-structure. The strength characteristics of sandstone are inversely proportional to the fractal dimension. The greater the uniaxial compressive strength and elastic modulus, the smaller the fractal dimension. The damage problem of sandstone can be characterized by critical damage value, which is proportional to the fractal dimension; the larger the fractal dimension, the more serious the internal damage of sandstone.

Rapid estimation of ductile crack formation in cross-wedge rolling

This study investigates the problem of predicting material cracking in cross-wedge rolling (CWR). Fifty-four cases were analyzed using the finite element method (FEM), and maximum values of the damage function were determined. Based on the results obtained from simulations, nomographs were created to allow for quick and easy determination of the maximum damage function values depending on the basic CWR parameters, mainly the forming angle, spreading angle of the wedge, and deformation ratio. The rotary compression test of a cylindrical sample was used to determine the critical damage values for the C45 grade steel formed in the temperature range 950–1150 °C. For the fracture condition to occur, it was assumed that the damage value should be higher than the critical damage value given by the damage function. This hypothesis was experimentally validated. The results of the experiments show good agreement with the numerical results of material fracture obtained with the method described in this study.

Investigation of punch shape design in tube hydro-piercing processes

This study is focused on punch shape design in tube hydro-piercing processes of SPFC590Y carbon steel tubes. The flow stresses of the carbon steel tubes obtained by tensile tests are used in the finite element simulations of tube hydro-piercing process with software “Deform 3D.” The ductile fracture criterion of Normalized Cockcroft and Latham is used during the FE simulations. The critical damage value for NCL fracture criterion is obtained by comparing simulation results and tensile test results. The effects of various parameters such as punch strokes, internal pressures, etc. on tube deformation and fracture mechanism in hydro-piercing processes are investigated. Hydro-piercing experiments are conducted. The characteristics of the experimentally pierced hole sections are compared with the simulation results to validate the analytical models. The effects of various parameters on the characteristics of pierced hole sections after hydro-piercing processes are discussed numerically and experimentally.

Influence of varying nitrogen on creep deformation and damage behaviour of type 316L in the framework of continuum damage mechanics approach

In the present study, Kachanov–Rabotnov continuum damage model has been employed to describe the steady state and tertiary creep deformation and damage behaviour of 316L austenitic stainless steel with different nitrogen contents of 0.07, 0.11 and 0.22 wt%, at 923 K. For all the nitrogen contents, the model appropriately predicts the creep strain–time data, creep rupture strain and rupture life. The model parameters such as characteristic strain and damage rates systematically decrease with the increase in nitrogen content. The derived iso-damage contours superimposed on creep strain–time data indicate that the evolution kinetics of strain, as well as damage, are unique at each applied stress level. For nitrogen added type 316L SS, the critical damage value ( ωcr) at which creep failure takes place is found to be less than 1 and is in the range of 0.35–0.60. It is observed that the dominance of damage rate ([Formula: see text]) over the strain rate ([Formula: see text]) increases with increasing nitrogen content from 0.07 to 0.22% N for the steel. A direct correlation has been established between the creep rupture ductility and the ratio of strain rate to damage rate, i.e. [Formula: see text]/[Formula: see text] using the Kachanov–Rabotnov model for different nitrogen contents and stress levels.

Rotary compression as a new calibration test for prediction of a critical damage value

The article presents the problem of ductile fracture of metals and metal alloys formed in hot working conditions. The basic damage criteria used in modelling fracture as well as calibrating tests used to determine the critical damage values were discussed. A concept of a new calibrating test based on rotary compression of a disc or a cylinder was presented. Using the proposed calibrating test along with nine damage criteria the critical damage values for 50HS (1.5026) grade steel, formed in the temperature range 950 °C to 1150 °C were determined. A significant dependency of the critical damage value on temperature was observed. The stress states occurring in rotary compression and the cross-wedge rolling, skew rolling in a two-roll rolling mill and helical-wedge rolling processes were compared. On the basis of the results obtained it was advised to apply rotary compression of a cylinder samples to determine the critical damage values used in the analyses of cross- and skew rolling.

Fracture and deformation characteristics of AZ31 magnesium alloy plate during tension rolling

The deformation and fracture behavior with tension force of AZ31 Mg alloy plate were investigated by hot compressive experiments, rolling process experiments and finite element simulation (with tension). The critical fracture strain (Cf) at the rolling deformation zone was discussed through the isopiestic method. The relationship between Cf and strain rate and the temperature was described by the Arrhenius mathematical model and Z parameter. Based on finite element methods (FEM) and simulated maximum damage value, the fracture criterion was expressed as a function of LnZ. The relationship between the average crack length (Lave) and LnZ was constructed to expound the fact that the critical damage value decreased with the augment of the Lave under the equal reduction. Though the simulation of tension rolling and analysis of stress state in rolling slip zone, the rolling force is reduced by applying tension, so as to reduce the friction force and restrain the cracking tendency of the plate.

Fracture criterion for predicting edge-cracking in Hot rolling of twin-roll casted AZ31 Mg alloy

Edge-cracking as one of main defects for rolled Mg alloy sheets is inevitable due to the combined characteristics of the material and process. This study aims to quantitatively analyze the damage distributions induced by rolling deformation in transverse direction (TD) for twin-roll casted (TRCed) AZ31 Mg alloy, and optimize the Freudenthal fracture criterion to predict the crack initiation and propagation during the hot rolling. FEM simulations and laboratory experiments of edge-cracking behaviors during the rolling process were carried out at temperatures of 250∼400 °C and reduction rates of 30%∼45%. Overall cracking indexes, including temperature- and reduction-dependent transverse depth of edge-cracking, distributions of damage based on the Freudenthal criterion, and critical damage values to fracture were discussed. Results show that the fracture mode of edge cracks is dominated by 45° crossed shear cracking in the longitudinal (RD–ND) section of rolled sheets, and the cracking depth along the TD increases as the rolling temperature decreases and reduction rate increases. The transverse damage decreases linearly from the edge to the interior during the rolling when using the Freudenthal criterion, which can be attributed to the combined effects of temperature difference and effective stress difference along the TD. The critical damage value of Freudenthal criterion was successfully obtained for establishing the criterion for edge-cracking prediction in AZ31 Mg alloy rolling, which is within the range of 0.59∼0.88 and has a clear linear relationship with Ln(Zener-Hollomon parameter, Z).

Прогнозування постпірогенного відпаду в сосняках, пошкоджених літніми низовими пожежами, у Лівобережному Лісостепу України

Пожежі є одними із найнебезпечніших чинників дестабілізації лісів. У зв’язку зі зростанням посушливості клімату ризик збільшення частоти й масштабів лісових пожеж залишається високим, тому актуальним є розроблення науково обґрунтованих заходів із пом’якшення екологічних, економічних та соціальних наслідків лісових пожеж. Удосконалено та уточнено показники, що характеризують візуальні прояви пошкодження дерев після низових пожеж, та показники вогнестійкості середньовікових дерев сосни звичайної (Pinus sylvestris L.). Виявлено, що в міру збільшення середньої висоти нагару на стовбурах зростає частка відпаду в досліджуваних групах дерев (r = 0,87, tф = 5,80, t0,01 = 3,17). Встановлено, що вогнестійкість дерев збільшується зі збільшенням природного ступеня товщини дерева в насадженні (виявлено обернений достовірний кореляційний зв’язок між природним ступенем товщини (ПСТ) і категорією санітарного стану пошкоджених дерев: (r = -0,54; р = 0,05). Розроблено прогностичну модель для встановлення ймовірності відпаду дерев, пошкоджених низовими стійкими літніми пожежами, яка як предиктори включає середню висоту нагару на стовбурах та ПСТ (точність прогностичної моделі становить понад 78 %).

Using high temperature tensile testing data to analyze hot formability of Sn-5Sb alloy: instability and critical damage criteria

In a general overview, hot workability defined by relative ease of deformation during thermomechanical processing depends on localized distribution of stress, strain, temperature and strain rate. In the current research, unsteady flow and formability behavior of Sn-5Sb alloy was investigated using hot tensile tests carried out on the homogenized cast material. To do this, occurrence of instability and evolution of microstructure of such alloy were studied taking the advantage of various instability criteria for hot deformation routes. The output of the models which can be categorized in analytical and empirical approaches were studied in detail and their performance and relative conservativeness and significance were compared. For a better clarification and cognitive comparison of obtained results, hot deformation processing maps were established based on data offered by diverse instability criteria. In addition, an attempt was made for determining critical damage values for this alloy during hot deformation considering several ductile fracture criteria. Taking the advantage of hot tensile data, the tests were then simulated for obtaining required characteristic stress and strain values to be used for evaluating ductile fracture. Simulations were performed by means of finite element method (FEM) in a three-dimensional state of strain in deformation zone. The results exhibit that critical damage values strongly depend on strain rate and temperature and is in accordance with flow instability variation in this alloy.

Investigation of failure during rubber pad forming of metallic bipolar plates

Abstract In this study, the forming of metallic bipolar plates micro-channel was investigated. Rubber pad forming process was employed to fabricate the parallel micro-channels. According to the experimental observation, the onset of failure was the main limiting factor during the deformation of micro-channels. Therefore, the fracture behavior was studied during rubber forming processes. Experimental analysis with the finite element model (FEM) simulation was adopted to investigate the fracture mechanism. Three different fracture criteria were used to predict the fracture. Critical damage values were determined through conducting the uniaxial tension test. The fracture surface was constructed using ductile fracture criteria, and the most accurate fracture prediction was obtained via normalized Cockroft-Latham fracture criterion (9.14% fracture prediction error). The effect of process parameters on stress triaxiality and normalized Lode angle parameter was analyzed by FEM simulation results. According to the results, process parameter variation did not significantly affect the stress state. Thus, the normalized Cockroft-Latham fracture criterion was employed to investigate the onset of fracture in different forming conditions and the effect of process parameters on damage evolution. Based on the findings, draft angle, corner radius, and the ratio of w/h should be set to 15°, 0.2 mm, and 1.6 in order to achieve 100% filling percentage.

Rotary compression in tool cavity\u2014a new ductile fracture calibration test

Ductile fracture is one of the most common failure modes in hot metal forming. It can be predicted by means of so-called damage functions that describe the relation between stress, deformation and fracture initiation. A practical use of these functions requires the knowledge of the critical damage value of the material that is determined by calibration tests based on compression, tension and torsion. For the prediction to be correct, one must ensure that the modelled and real stresses are in agreement. Previous studies did not offer any effective test for determining critical values of damage under changing load conditions that occur in cross and skew rolling processes, among others. To compensate for this knowledge gap, researchers at the Lublin University of Technology have developed a new test consisting in rotary compression of a test-piece in a cavity between the tools, which is described in this paper. In the proposed test, a cylindrical test-piece is rolled over a cavity (impression) created by grooves on two mating tools. The cavity height is smaller than the test-piece diameter. At the critical value of the forming length, the state of stress induced thereby in the test-piece axis causes fracture. Knowing the critical forming length, it is possible to determine the critical value of damage by numerical modelling. The practical application of the proposed test is illustrated through the case of C45 grade steel subjected to forming in the temperature range 950–1150 °C. The analysis makes use of the normalized Cockcroft-Latham (NCL) criterion of ductile fracture.

Fracture analysis on U-bending of AA6061 aluminum alloy sheet using phenomenological ductile fracture criteria

Abstract In this study, three ductile fracture criteria were used to investigate the fracture in U-bending of AA6061-T6 aluminum alloy sheets. Considering the importance of the calibration procedure, three different tension tests including the uniaxial, plane strain, and notched tensions were conducted based on the stress state analysis. The Ayada, Rice-Tracey, and normalized Cockroft-Latham fracture criteria were calibrated through a hybrid experimental-numerical method to determine their critical damage values. Fracture envelopes (i.e., the locus of fracture strains) were constructed for the investigated fracture criteria based on the results of various tension tests in their calibration procedure. The calibrated fracture criteria were implemented in the commercial finite element (FE) code Abaqus/Explicit using an appropriate user subroutine. The numerical simulation of the bending process was performed and validated by relevant experiments. The accuracy of the fracture criteria was investigated by comparing fracture displacements predicted using the FE model with those measured by experiments. According to the obtained results, variations of damage function (fracture criteria) and the type of the calibration test utilized for a certain fracture criterion have significant effects on the critical damage value, the fracture envelope, and the accuracy of the fracture prediction. For all investigated criteria, the prediction is reasonable when the critical damage value was calibrated under the plane-strain tension. Thus, the plane strain tension is the best calibration method for predicting fracture in the U-bending process. The most accurate fracture prediction is obtained by normalized Cockroft-Latham fracture criterion, which was calibrated by the plane strain tension test with 2.52% error in fracture prediction. However, the prediction of fracture displacement in U-bending process is very imprecise and strongly overestimated, when the uniaxial tension was used as the calibration test. The Ayada criterion has the lowest error of 11.83% for predicting the fracture displacement when the uniaxial tension test was used as a calibration method. Also, the maximum prediction error (the lowest accuracy) was found to be 51.97% by the normalized Cockroft-Latham criterion calibrated under the uniaxial tension test. Globally, for the U-bending process, it is recommended to calibrate the critical damage values under the plane strain condition. But, when only the uniaxial tension test is available, the Ayada fracture criterion gives the best prediction.

Failure Prediction Capability of Generalized Plastic Work Criterion

In this study, failure prediction capability of the generalized plastic work criterion was evaluated. Criterion was applied to the uniaxial tensile and Nakajima stretch forming tests to predict the forming limits of an advanced high strength steel sheet. Firstly, critical damage value of the material was calculated for two different cases. Energy value till uniform elongation range was considered for in the first case, while total energy value was considered in the second case. Finite element simulations of the uniaxial tensile and Nakajima stretch forming tests were performed for both cases. The fracture strain in the uniaxial tensile test and limit strains of each Nakajima sample were predicted and the predicted results were compared with the experimental results. Comparisons showed that the onset of the diffuse necking and the fracture strain were predicted successfully in the uniaxial tensile test. However, it was observed from Nakajima tests that limit strains at the left side of the forming limit diagram (FLD) were predicted successfully by the criterion, while they weren’t accurately predicted at the right side of the FLD.

Determination of the critical value of damage in a channel-die rotational compression test

This article describes the problems involved in modelling material cracking in skew rolling processes. The use of the popular damage criteria is impossible because of the lack of a calibration test that would make it possible to determine the critical value of material damage under conditions similar to those found in skew rolling. To fill this gap, a test called channel-die rotational compression was proposed. It consisted of rolling a disk-shaped specimen in a cavity created by two channels of cooperating tools (flat dies), which had heights smaller than the diameter of the specimen. When the rolling path was sufficiently long, a crack formed in the axial zone of the specimen. In this test, modelling using the finite element method made it possible to determine the critical values of material damage. As an illustration, the test was used to determine the critical damage value when conducting a rotational compression process on 50HS steel (1.5026) specimens formed in the temperature range of 950–1200 °C. The analysis was conducted using the Cockcroft–Latham damage criterion.

Assessment of ductile fracture criteria with respect to their application in the modeling of cross wedge rolling

Ductile fracture is a common failure mode in cross wedge rolling (CWR) and can be predicted by analyzing material damage functions. This paper describes 10 such functions. To determine the moment of fracture, one must know the critical damage function which is calculated via calibration test. It is vital to ensure that the stress state during calibration is as close as possible to the real stress. Since there are no calibration tests dedicated to cross rolling processes, a new test has been devised, based on a rotary compression process for cylindrical samples. Using the proposed calibration test and 10 fracture criteria, the critical damage values of C45 steel deformed at 1150 °C are determined. Next, CWR tests are performed using technological parameters conducive to crack formation in the axial region of the formed step on the workpiece. Numerical and experimental results of the moment of crack initiation and its length are compared, and – as a result – 4 damage criteria that best predict material fracture are selected.

Prediction of Crack Formation for Cross Wedge Rolling of Harrow Tooth Preform

The article presents the issue of material fracture during the process of cross-wedge rolling (CWR). The object of the research was the process of forming a harrow tooth preform. In the conducted analysis nine damage criteria were applied. The critical value of damage was determined with a new calibrating test, basing on rotational compression of a sample in a channel. The results of calculations were compared to the results of experimental testing performed in laboratory conditions in Lublin University of Technology. On the basis of the obtained results an assessment of the applied damage criteria and their applicability in the analysis of CWR processes was conducted.