Ductile-brittle Transition Behavior Research Articles

Realizing the outstanding strength-toughness combination of API X65 steel by constructing lamellar grain structure

The development of pipeline steels with exceptional cryogenic toughness is deemed imperative for their applications in various engineering fields. In this work, API X65 steel with lamellar grain (LG) structure is constructed through warm deformation techniques. Comparative analysis with raw API X65 steel revealed notable enhancements in both yield strength (YS) and ultimate strength (UTS), exhibiting increments of 315 MPa and 164 MPa, respectively, while retaining substantial fracture toughness (KIc = 251.14 MPa m0.5). Remarkably, the LG steel exhibits a distinct absence of a ductile-brittle transition behavior over a wide temperature range, maintaining an exceptionally high impact energy from room temperature (RT) to liquid nitrogen temperature (LNT), and the Charpy impact energy exceeding 330 J at LNT, nearly 16 times higher than the raw API X65 steel. This performance can be primarily attributed to the superior plastic deformation capability, coupled with the delamination toughening mechanism. The resultant tortuous path of crack propagation effectively facilitates the absorption of substantial energy, decreases notch tip sensitivity depending on the temperature, stress triaxiality, and strain rate, thereby fostering excellent cryogenic toughness.

Effect of Chemical Corrosion on Rock Fracture Behavior in Coastal Deep Mines: Insights from Mechanical and Acoustic Characteristics

The demand for critical minerals has increased extraction activities in coastal deep mines where challenges such as high stresses, chemical corrosion, and mining disturbance impacts are present. This study investigated the effects of chemical corrosion and confining pressure on the mechanical and fracture behaviors of granite specimens, which are crucial for ensuring the stability of surrounding rock in coastal deep mines. Triaxial compression tests were conducted on uncorroded specimens and corroded specimens immersed in acid and alkali solutions under varying confining pressures, with real-time acoustic emission (AE) monitoring. Based on the test results, the strength and deformation properties, progressive fracture, and failure processes, as well as the AE response characteristics of the specimens under chemical corrosion and confining pressure were analyzed. Additionally, the influence of confining pressure on the chemical damage and brittle–ductile transition behavior of specimens was discussed, and the mechanism of chemical corrosion on the physical and mechanical behavior of specimens was revealed based on mineralogical analysis. These findings underscore the importance of understanding the interplay between chemical corrosion, confining pressure, and rock fracture behavior in coastal deep mining and contribute to evaluating the stability of underground surrounding rocks under corrosion environments.

Enhancing the Tensile Properties and Ductile-Brittle Transition Behavior of the EN S355 Grade Rolled Steel via Cost-Saving Processing Routes.

Structural rolled steels are the primary products of modern ferrous metallurgy. Consequently, enhancing the mechanical properties of rolled steel using energy-saving processing routes without furnace heating for additional heat treatment is advisable. This study compared the effect on the mechanical properties of structural steel for different processing routes, like conventional hot rolling, normalizing rolling, thermo-mechanically controlled processing (TMCP), and TMCP with accelerating cooling (AC) to 550 °C or 460 °C. The material studied was a 20 mm-thick sheet of S355N grade (EN 10025) made of low-carbon (V+Nb+Al)-micro-alloyed steel. The research methodology included standard mechanical testing and microstructure characterization using optical microscopy, scanning and transmission electronic microscopies, energy dispersive X-ray spectrometry, and X-ray diffraction. It was found that using different processing routes could increase the mechanical properties of the steel sheets from S355N to S550QL1 grade without additional heat treatment costs. TMCP followed by AC to 550 °C ensured the best combination of strength and cold-temperature resistance due to formation of a quasi-polygonal/acicular ferrite structure with minor fractions of dispersed pearlite and martensite/austenite islands. The contribution of different structural factors to the yield tensile strength and ductile-brittle transition temperature of steel was analyzed using theoretical calculations. The calculated results complied well with the experimental data. The effectiveness of the cost-saving processing routes which may bring definite economic benefits is concluded.

Determination of the ductile-to-brittle transition temperature of NIOMOL 490 K steel welded joints

This paper is dedicated to the ductile–brittle transition behaviour of the microalloyed structural steel NIOMOL 490 K. This steel grade is used for welded pressure vessels subjected to dynamic loads and operating at sub-zero temperatures. Therefore, it must have an acceptable toughness. Due to its importance for the safety assessment of pressure vessels, a characterization of this steel was carried out using the Charpy V-notch impact test in the temperature range between −60 °C and + 60 °C. The notches were located in parent material, heat affected zone and weld metal. In this paper, the tensile strength properties at ambient temperature and the nil ductility temperature in the temperature range from −60 °C to + 60 °C are presented.

A theoretical and experimental investigation on the surface formation mechanism in elliptical vibration cutting of single crystal magnesium fluoride

Manufacturing precise microstructures on magnesium fluoride surface remains challenging due to its brittleness and anisotropy. This study investigates the surface formation mechanism in ductile machining of single crystal magnesium fluoride and explores the feasibility of fabricating sophisticated microstructures on magnesium fluoride surfaces by applying elliptical vibration cutting technology. We conducted a systematic study on the ductile-brittle transition behavior, material removal mechanism, and fabrication performance of microstructures through theoretical analysis and cutting experiments. A theoretical model that takes into account the elliptical trajectory's orientation angle has been established to determine the evolution of instantaneous uncut chip thickness and the characteristic nominal depth of cut in one cycle during elliptical vibration cutting. By comprehensively examining the influence of the elliptical trajectory, determined by vibration amplitudes, orientation angle, and nominal cutting speed, on the dynamic behaviour of the ductile-brittle transition, we verified the proposed theoretical model with convincing experimental results. Larger critical depth of cut for ductile-brittle transition and smaller cutting forces achieved by EVC contribute to the improved ductile machinability of MgF2. With optimal vibration parameters, the critical depth of cut increases by 56 times compared to ordinary cutting. Theoretical findings regarding plastic deformation parameters and cleavage fracture parameters align well with experimental observations, providing a more comprehensive understanding of the anisotropy influence on damage evolution during the surface formation in elliptical vibration cutting of magnesium fluoride. Furthermore, leveraging our fundamental understanding of material removal and surface formation mechanisms, we successfully generated bi-sinusoidal arrays on magnesium fluoride surfaces with exceptional accuracy (machining error < 1.5%) and high efficiency (machining time < 121.5 min) by applying elliptical vibration cutting.

Carbon sequestration reservoir at Rock Springs Uplift, Wyoming, USA

The Rock Springs Uplift (RSU) located in southwest Wyoming USA as indicated in Figure 1 is one of several sites across the country to be characterized for suitability for CO2 sequestration. The RSU was identified for several reasons: proximity to a large CO2 emissions point source, the overall geometry of the RSU structure, and geologic formations recognized to have properties required for long term storage of CO2. Original rock cores of the Weber Sandstone formation and the dolomite facies of the Madison Limestone formation from the RSU were prepared into 25-mm diameter rock samples. These samples were vacuum-saturated to 100% saturation with synthetic brine, aged with brine for 800 hours at in-situ temperatures and initial confining pressure of 3.5 MPa, and aged with CO2-rich brine (400 hours first with brine and another 400 hours with compressed CO2-saturated brine) at in-situ temperatures and initial confining pressure of 3.5 MPa. During the aging process, the pore and confining pressure were increased in small steps, typically 0.69 to 1.38 MPa at a time using high precision syringe pumps (Teledyne ISCO 260D, Lincoln, NE, USA) until the test conditions were met without fluid flow. Laboratory hydrostatic and triaxial experiments were performed at in-situ reservoir conditions with the temperatures of 90°C for Weber Sandstone and and 93°C for Madison Limestone under three differential pressures of 6.9 MPa, 34.5 MPa and 55.2 MPa.&#x0D; Geomechanical results of the aged rock samples are presented and discussed. Under the triaxial compression, Weber Sandstone exhibited brittle failure strengths while Madison Limestone exhibited a brittle-ductile transition behavior. For the sandstone samples with similar initial porosity, the Young’s moduli increased and Poisson’s ratios decreased as the result of CO2 under the linear elastic regime. No relationship between stress (or strain) data and CO2 in the nonlinear plastic regime was observed. However, the confining pressure has a greater effect than CO2 on geomechanical behaviors. For the limestone samples, the change of elastic constants due to CO2 is more significant than that of sandstone samples. However, no consistent trend was observed on the limestone samples,&#x0D; and the effect of CO2 is not the dominant factor influencing the plastic properties of rocks. DH1c with the lowest initial porosity and differential pressure exhibits the highest peak strength, Young’s modulus and Poisson’s ratio, indicating the effect of initial porosity. Considering the effect of CO2 on Mohr failure envelopes, the decreasing trend of cohesion and increasing friction angle was observed in both sandstone and limestone samples. Table 1 summarizes the maximum deviatoric stress, elastic properties, and shear strength parameters of Weber Sandstone and Madison Limestone samples.

Microstructure evolution and mechanical properties of directionally solidified Al0.5CoCr1.3FeNi1.3(Ti, Si, B, C)0.3 multiphase complex concentrated alloy

Microstructure evolution and mechanical properties of Al0.5CoCr1.3FeNi1.3(Ti, Si, B, C)0.3 multiphase complex concentrated alloy (CCA) prepared by directional solidification combined with quenching during solidification (QDS) technique were studied. The directionally solidified (DS) samples were prepared at constant growth rates V ranging from 2.78 × 10−6 to 5.56 × 10−5 m/s, the constant temperature gradient in liquid at the solid-liquid interface of GL = 16.5 × 103 °C/m and then quenched at a cooling rate of about 50 °C/s. The solidification of the studied CCA begins with the growth of columnar FCC(A1) dendrites and is finalised by the formation of a multiphase microstructure in the interdendritic region. The DS samples subjected to isothermal annealing at 900 °C for 25 h show a strong brittle-ductile transition (BDT) behaviour characterised by brittle-ductile transition temperature (BDTT) between 650 and 700 °C at a strain rate of 1 × 10−4 s−1. The tensile deformation curves show only a strain hardening stage at test temperatures up to 650 °C. At temperatures ranging from 750 to 900 °C, the alloy shows anomalous strain hardening behaviour characterised by one strain hardening stage and three well-distinguished strain softening stages.

Temperature gradient induced tough-brittle transition behavior of a high-strength Al-4.2Mg-0.4Sc-0.2Zr alloy fabricated by laser powder bed fusion additive manufacturing

The complex process and thermal behavior of laser additive manufacturing will lead to complex microstructure and property evolution. In order to enhance the processing efficiency of a high-strength Al-4.2Mg-0.4Sc-0.2Zr alloy fabricated by laser powder bed fusion (LPBF) additive manufacturing, a temperature gradient induced ductile-brittle transition behavior caused by changes in laser scanning speed for LPBF processed Al-4.2Mg-0.4Sc-0.2Zr alloy was reported in this study. As the laser scan speed increased from 0.4 ms-1 to 2.4 ms-1, a transition in fracture mode from toughness to brittleness was observed, where the tensile strength was decreased from 547.6 MPa to 472.3 MPa while the elongation decreased from 13.8% to 1.9%. Based on transmission electron microscopy (TEM) and electron backscatter diffraction (EBSD) characterizations, it was attributed to the cross-scale different microstructures from mesoscopic to microscopic as laser scan speed increased, including (i) more porosity in microscale (~30 μm), (ii) slenderer coarse grains and narrow equiaxed grain regions within melt pools in sub-microscale (~1 μm) and (iii) suppression of the Mg segregation along grain boundaries and formation of higher dislocation densities and stacking faults in the nanoscale (~200 nm). These changes in the microstructure caused the specimens processed with high scan speeds (above 1.6 ms-1) to be more prone to initiation of cracks during tensile, the ability of synergistic deformation between grains to decrease, and the bonding strength between grains to reduce. By simulating the thermal field of the melt pool, the formation mechanism of the different microstructures was ascribed to the different temperature gradients, which further determined the grain structures and element distributions. This work demonstrated that the structure and properties of LPBF processed high-performance Al alloys can be well tailored by processing parameter control.

Ultra-precision cutting characteristics of binderless tungsten carbide by in-heat-process laser-assisted diamond machining

The study systematically investigates the ductile-brittle transition behavior, material removal mechanism, and end-face turning performance of binderless tungsten carbide using in-process-heat laser-assisted diamond machining. Both numerical simulation analysis and experimental cutting experiments were conducted. To ensure that the laser loading condition and energy distribution were consistent with the ray-tracing simulation and spatial power density distribution measurement, a practical thermal simulation model was created with a semicircular Gaussian distribution. This model was then used to study the temperature distribution, and the material's thermal transient response to laser radiation was also analyzed in detail. The high-temperature nanoindentation revealed increased ductile machinability due to plastic deformation, microhardness reduction, and Young's modulus decrease at elevated temperatures, providing fundamental support for the ductile-brittle transition behavior. The ductile-brittle transition depth increased by 247.20% compared to conventional groove cutting without laser assistance. The cutting forces during groove cutting decreased gradually with increasing laser power, but excess laser power may cause fluctuations in cutting forces due to surface high-temperature oxidation and potential thermal expansion. The ductile-brittle transition dynamic behavior analysis, based on the discrete wavelet transform algorithm, showed good consistency with the conventional groove profile analysis. The friction coefficient between the tool rake face and chip decreased with increasing laser power, which facilitated improving the tool life. The statistical analysis of end-face turning experiments based on the Taguchi method indicated that laser power was the most significant factor affecting surface quality. The verification turning experiments validated the determined optimal parametric combination. Ultra-high-quality spherical lenses were obtained in ductile cutting mode with slightly less tool wear, a more homogeneous finish (less than 3 nm in Sa), and more outstanding form accuracy (133 nm in PV) compared to conventional turning without laser assistance.

Brittle‒ductile transition behavior of 6H-SiC in oblique diamond cutting

6H-SiC is a typical hard-brittle material, and the challenge of performing ductile-regime machining in diamond cutting necessitates an in-depth understanding of the brittle‒ductile transition (BDT) mechanism. In this work, a novel machining method named oblique diamond cutting is employed to improve the BDT behavior of 6H-SiC. First, the tool edge ovalization effect is proposed, which provides deeper insight into the change in cutting edge shape evaluated in the cutting plane. An empirical model under the combined influence of the nominal tool rake angle, tool sharpness and tool inclination angle is established to effectively describe the equivalent cutting edge radius of the elliptic-shaped cutting edge in the cutting plane. When the tool inclination angle was increased from 0° to 45°, the equivalent cutting edge radius increases gradually, and the error of the prediction model remained at a low level of less than 7.5%. Second, an oblique plunge cutting experiment and finite element (FE) simulation were carried out under the consideration of tool edge ovalization effect. The simulation results indicate that the BDT depth grew gradually as the tool inclination angle increased, and shows the same changing trend as the experimental results with an average error of 14.9%. When the tool inclination angle was increased to 45°, the BDT depth obtained in experiments doubled (dc = 42.4 nm) compared to the results of traditional orthogonal cutting including from the references and this work. Such a huge improvement in the BDT behavior in cutting is of great significance for the successful execution of ductile-regime machining on a SiC optical component in practice. Finally, the reason for the increase in the BDT depth is revealed to result from changes in the stress distribution in the cutting area due to the increasing equivalent cutting edge radius of the elliptic-shaped cutting edge arc, especially the tensile stress, which is particularly sensitive to brittle materials with insufficient tensile strength. Compared to traditional orthogonal cutting, a high compressive stress zone is formed beneath the tool because more materials undergo the squeezing of the elliptic-shaped cutting edge. Thus, the tensile stress concentrated on the machined surface behind the cutting edge is suppressed, which is beneficial for promoting the plastic deformation of brittle materials with insufficient tensile strength. This is of great significance not only for SiC but also for the processing of other hard-brittle materials.

Theoretical and experimental investigations of surface generation induced by ultrasonic assisted grinding

Ultrasonic assisted machining has been proved to have good performance for difficult to cut materials. Due to the complex contact between abrasives and workpiece, in-depth insight of material removal process of ultrasonic assisted grinding (UAG) is still challenging. In this investigation, ultrasonic surface texture is studied considering the effects of the grinding wheel topography, brittle-ductile transition behavior and ultrasonic vibration. A novel theoretical model of the grinding wheel topography is reconstructed considering the shape, size and random arrangement of abrasives. Based on this, surface topography prediction is conducted by the numerical method. The simulation analysis demonstrated that interference and self-interference of abrasive grits induced by ultrasonic vibration are the primary patterns, which explains the material removal mechanism in the UAG process. Furthermore, the grinding damages of the brittle and ductile grinding are parameterized based on different brittle and hard nature. Surface topography and surface roughness are predicted and analyzed by comparisons of simulation and experimental results. Those models proposed in this paper have potential for in-depth understanding the material removal process and optimizing the process parameters of the UAG process.

Investigation on brittle-ductile transition of PMMA mode-II fracture using time-temperature superposition principle

The rate-temperature dependent brittle-ductile transition (BDT) behavior of PMMA (polymethyl methacrylate) mode-II fracture was investigated through tensile-loading shear fracture (TLSF) tests. The dimensionless ratio KJC/KIIC was chosen as the index to identify the brittle/ductile state. Assuming the fracture property to be viscosity-dominated, the time-temperature superposition principle based on the Arrhenius equation was adopted. The master curves of KJC/KIIC in a wide range of loading rate and temperature were constructed with the experimental data obtained under limited test conditions. With the derived critical BDT band from the master curve, the BDT state of PMMA’s fracture under complex loading conditions was successfully predicted and experimentally validated. The results are helpful to describe the BDT behavior and provide an equivalent approach to investigate the mode-II fracture which can substantially save the experimental cost and time.

On crack suppression mechanisms of ultrasonic elliptical vibration cutting of 3Y-TZP ceramics

Ultrasonic elliptical vibration cutting (UEVC) is a promising technique to realize the crack-free machining of ceramic materials. However, the underlying crack suppression mechanism and its impact on the ductile-brittle transition (DBT) behavior of ceramics still remain poorly understood. In the current work, the material removal characteristics of 3Y-TZP ceramics under UEVC, including the crack propagation process, stress distribution condition, and critical transition depth, were rigorously studied by using both the smoothed particle hydrodynamics (SPH) simulation and the experimental method. It was found that the material removal behavior and critical transition depth were highly related to the ultrasonic speed ratio (Rs) that defines the ratio of the nominal cutting speed to the maximum ultrasonic velocity along the cutting direction. A critical (Rs) value of 0.128 was determined by the analytical method, beyond which the crack suppression mechanism of UEVC is mainly due to the time-varying cutting speed and angle. When the Rs is lower than the critical value, the reduction of the effective cutting thickness caused by the overlapping trajectory becomes a dominant factor in enlarging the ductile regime and in improving the machining quality of 3Y-TZP ceramics.

Adjustable brittle-ductile transition behavior and rheological behavior of polypropylene random copolymer nanocomposites through well interfacial-loaded nanoparticles

To improve the low-temperature toughness of polypropylene random copolymer (PPR), a series of PPR/ethylene-propylene rubber/silica (PPR/EPR/SiO2) nanocomposites were prepared through toughening strategy based on interfacial-loaded particles and adjustable dispersed phase. The results showed that the brittle-ductile transition behavior for PPR/EPR/SiO2 nanocomposites could be adjusted by silica and rubber contents, and consequently the composites were endowed with excellent low-temperature impact resistance. Furthermore, the nanocomposites never presented the significant deterioration of rigidity compared with pure PPR. The dynamic rheological results showed that viscosity change in PPR matrix and EPR phase could make silica particles preferentially locate at PPR-EPR interface, which strongly reduced the size of EPR domain and consequently led to a stronger shape relaxation of long-time scale. According to dynamic rheological behavior, microstructure and interparticle distance analysis of PPR nanocomposites, the adjustable brittle-ductile transition behavior was ascribed to the reduced rubber interparticle distance coming from the well interfacial-loaded nanoparticles.

Determination of ductile-to-brittle transition temperature of NIOMOL 490K steel welded joints

This paper is devoted to the ductile–brittle transition behavior of high strength low alloyed structural steel NIOMOL 490K. This steel grade is designed for welded pressure vessels exposed to dynamic loads, operating at temperatures below zero, and that is why it must have acceptable toughness. Due to its importance for the safety assessment of pressure vessels, a characterization of this steel with Charpy V-notch test in range of temperature between-60 ⁰C and +60 ⁰C was undertaken. Ductile-to-brittle transition temperature curves were generated in the present study by using instrumented Charpy pendulum impact test on V-notch specimens. Notches were located in the parent material, heat-affected zone and weld metal. The nil-ductility temperature and tensile properties in temperature range from -60 ⁰C to +60 ⁰C are presented in this paper. We used different test temperatures to better understand ductile-to brittle transition response than just use either Charpy energy or other related ductility criteria.

Характеристики кривых ударного нагружения и их взаимосвязь с параметрами излома образцов стали 32Г2Р

Impact tests are mandatory for a wide range of structural steel products to evaluate the required service life and operational safety. This test is especially relevant for products used in operation in climatic areas with a cold climate, since it allows one to determine the temperature range of the ductile-brittle transition. Depending on the structural-phase state of a metal, the type of the temperature relationship of impact toughness and its displacement on the temperature axis may differ significantly. For ductile materials, the temperature range of the ductile-brittle transition is shifted towards ultra-low negative temperatures whereas for materials in the embrittled condition it lies in the region of higher temperatures. Ductile-brittle transition behavior of medium-carbon steel with 0.32 % C-1.35 % Mn-0.003 % B in two conditions (after normalization and after quenching and tempering) by instrumented impact testing and fracture analysis was studied. On the descending branch of the force-displacement curves the periods corresponding to different zones of propagation of the main crack are distinguished: period I is the ductile zone of pure shear, period II is the zone of brittle fracture, period III is the ductile zone of break fracture. Each period can be quantitatively described by a set of strength, plastic and gradient parameters. It is established that the displacement to the beginning of linear period II (SIIb) and slope of the curve on it (ΔF / ΔS)II have a better correlation with shear fracture zone percentage (B) than the other distinguished parameters of force-displacement curves.

Ductile-Brittle Transition Behaviour of Lithium Metasilicate/Disilicate Glass-Ceramics in Diamond Grinding

Lithium metasilicate/disilicate glass-ceramics (LMGC/LDGC) are attractive composite materials for all-ceramic dental restorations due to their promising strength and biocompatibility. However, their strong mechanical properties make it hard to machine with current dental chairside CAD/CAM-milling. The root cause is the unclarity of their mechanical behaviour under dynamic abrasive machining. This paper conducted single-diamond scratching experiments on LMGC and LDGC to extract the actual diamond grain-material contact in grinding to understand their ductile-brittle transition behaviour. Scanning electronic microscopy (SEM) observation was performed to identify the fully-ductile, ductile-brittle and fully-brittle regimes of the two studied materials. 3D laser confocal microscopy (LCM) was used to measure the critical cutting depths for these regimes. The critical cutting depths for fully-ductile and fully-brittle regimes are 89 nm and 133 nm for LMGC, and 209 nm and 428 nm for LDGC, respectively. These results provide an in-depth understanding of ductile-brittle transition behaviour of LMGC/LDGC under abrasive machining and a guidance for dental technicians to choose proper machining conditions for high-quality LDGC restorations.

Abnormal brittle-ductile transition for glassy polymers after free and constrained melt stretching: The role of molecular alignment

By comparing the brittle-ductile transition (BDT) behavior between uniaxial width-Free Melt pre-Stretched (FMS) and width-Constrained Melt pre-Stretched (CMS) poly(methyl methacrylate) (PMMA), the effect of molecular alignment on the mechanical response of glassy polymers has been investigated. Unexpectedly, during further mechanical characterization, CMS samples exhibit higher ductility than FMS samples along both the machine (stretching) direction (MD) and the transverse direction (TD). Combining the results from molecular orientation and stress relaxation, it is proposed that chain stretching and aligned chain density is responsible for the ductile deformation along the MD and TD, respectively. Along the MD, CMS samples exhibit more significant chain stretching than FMS samples due to width constraint, leading to a lower chain activation energy barrier in CMS samples. Upon further deformation, chain activation is then accelerated and shear yielding can be achieved at lower temperature. Along the TD, the orientation function remains constant for CMS samples but negatively increases for FMS samples, and the lower aligned chain density in FMS samples increases the activation energy barrier for plastic deformation. As a result, crazing prevails during further deformation for FMS samples and causes weaker ductility. The mode of BDT in glassy polymers is considered from multiple scales.

Brittle-ductile failure transition in geomaterials modeled by a modified phase-field method with a varying damage-driving energy coefficient

With elevated confining pressure and low temperatures, geomaterials may exhibit brittle-to-ductile failure transition due to increased cataclastic flow. In this work, we propose a modified phase-field damage model to capture this transition, wherein a portion χf of the plastic work that contributes to the fracture driving force, is assumed. In particular, we propose to compute χf based on a specific normalized stress parameter based on Byerlee's rule, which ranges from brittle tension fracture to cataclastic flow. In the former case, all the stored plastic free energy is assumed to contribute to fracture. However, in all other cases, the brittle fracture process at the macroscale is gradually suppressed with the increase of pressure, rendering a smaller value of χf. The proposed model includes eight material parameters, all of which can be calibrated from standard laboratory tests, i.e., conventional triaxial compressive experiments. To validate the performance of the proposed model, three pre-cracked specimens are constructed under plane strain conditions. Numerical simulations show that the predicted failure patterns agree with the experimental testing, which highlights the predictive capability of the model to capture brittle and ductile failure mechanisms. In addition, the proposed model can describe the brittle-ductile failure transition behavior in the homogeneous case and can predict the realistic failure process at the structural level.

Understanding the brittle-ductile transition of glass polymer on mesoscopic scale by in-situ small angle X-ray scattering

The structural evolution of poly (methyl methacrylate) (PMMA) under uniaxial stretching has been studied with in-situ synchrotron radiation small angle X-ray scattering (SAXS) to reveal the brittle-ductile transition (BDT) mechanism. The scattering invariant analysis method was applied to semi-quantitatively analyze the evolution of crazing. For the sample without melt pre-stretching, which exhibits almost the same BDT behavior in different directions. The formed crazes are enabled to grow and propagate stably via shear deformation of the matrix. While for samples with melt pre-stretching, crazing is further promoted when stretching along the transverse direction. With a higher craze growth rate and lower craze fibril fraction, the destructive crazing cannot be fully stabilized by shear banding and premature craze fracture occurs. In contrast, shear banding dominates the deformation when stretching along the pre-stretching direction. Due to the low craze concentration and slow craze growth rate, crazes with higher fibril fraction gradually slip with matrix shearing. The premature craze damage is consequently avoided and an enhanced toughness is achieved. The structural evolution of these samples indicates that the kinetic competition between crazing and shear banding is the key to the macroscopic toughness of glass polymers.