Tensile Strength Distribution Research Articles

Polydopamine modified carbon fiber to improve the comprehensive properties of carbon paper for proton exchange membrane fuel cell

In this study, polydopamine (PDA) was used to modify functional groups on the surface of carbon fiber (CF), and the effects of different dopamine hydrochloride (DPH) concentrations on the surface morphology, functional groups, contact angle and dispersion stability of CF were studied. Subsequently, the raw carbon paper (RCP), hot-pressed carbon paper (HPCP) and carbon paper (CP) were prepared successively using the modified CF through wet forming, impregnation/hot-pressing, and carbonization methods. The surface morphology, tensile strength, flexural strength, electrical resistivity, air permeability and pore size distribution were analyzed for these materials. It was observed that the introduction of −OH and − NH2 groups improved the hydrophilicity and dispersion of PDA modified CFs, resulting in an increase in formation index (FI) from 39.2 to 48.1 for RCP samples. With increasing DPH concentration, the tensile strength of CP initially increased but then decreased while its electrical resistivity showed an opposite trend. Finally, PDA modified CP was assembled into proton exchange membrane fuel cells (PEMFC). The PEMFC assembled from DPH-CP-2.5 achieved a maximum limiting current density of 1440.0 mA/cm2 and power density of 458.25 mW/cm2. Meanwhile, the lower material transmission impedance for DPH-CP-2.5 as well as excellent water management ability and gas transmission performance.

A Holistic Isotopic and Mineralogical Investigation of Ancient Thasos Theatre: Technology and Provenance of Thasos Marbles

The Stable Isotope Unit of the National Centre of Scientific Research and the Ephorate of Kavala and Thasos collaborated on a project to investigate construction materials from the Ancient Theatre on Thasos Island, which was funded by NSRF European funds (2007-2013 and 2014-2020). Bulk samples of marble were collected to determine their provenance, technology, degradation features, and mechanical and physicochemical properties, with the ultimate goal of developing a conservation plan. By utilizing novel scientific techniques, the research team was able to date constructions discovered within excavations and establish remedial and preventive conservation plans using marble technology. The samples were characterized in terms of their isotopic, chemical, and mineralogical composition. Additionally, extended physicochemical and mechanical testing was applied to estimate the current condition of the Ancient Thasos Theatre. The 13C and 18O isotopic composition of the calcitic marbles was analysed to determine the environmental conditions during calcite formation, making it possible to define the marble provenance. Compositional and morphological analyses were achieved using energy-dispersive X-ray analysis by scanning electron microscopy, while the mineralogical phases were detected using X-ray diffraction and petrographic (polarized optical microscopy) analysis. Mechanical testing according to European Standards was achieved through the examination of compressive tensile strength and grain size distribution.

Enhanced resistance to desiccation cracking of polymer–bentonite mixtures: an experimental investigation of underlying mechanisms

Polymers have been shown to enhance the resistance of swelling clay soils to desiccation cracking, a critical property in engineering applications, particularly in waste containment facilities. However, the microscopic and macroscopic mechanisms driving this improvement remain poorly understood. Additionally, the influence of different mixing methods on these mechanisms is not well-established. While dry mixing (DM) is more convenient for onsite implementation, wet mixing (WM) offers intercalation between clay and polymer, resulting in potentially more durable stabilization outcomes. In this paper, key properties related to desiccation cracking of a polymer–clay mixture were measured. The mixture was synthesized by amending Na-bentonite with sodium carboxymethyl cellulose (Na-CMC) using DM and WM. Soil water-retention characteristics curves (SWCC), swelling and shrinkage potential, tensile strength, and pore-size distribution by mercury intrusion porosimetry (MIP) were measured for both mixtures and untreated bentonite. Compared to pure bentonite, mixtures were found to have slightly reduced air-entry values, significantly lower swelling and shrinkage potentials, and higher tensile strengths. In all experiments, DM exhibited superior performance compared to WM. MIP analysis of the amended mixtures revealed a more porous structure compared to untreated bentonite.

A Review on Distribution of Reinforcement and tensile Strength of Aluminum Lithium Alloy based Nano Metal Matrix Composites Fabricated by STIR Casting

Aluminum Alloy (AA) parts are employed in lightweight engineering fields and have poor mechanical, wear, and corrosion resistance. Aluminum Matrix Composites (AMCs) are materials created by incorporating hard reinforcing particles into an aluminum matrix alloy. The new material has improved characteristics, including higher specific stiffness and strength, as well as higher corrosion resistance, elastic modulus, wear resistance, and low weight. Metal Matrix Composites (MMCs) are composite materials in which metal serves as the matrix and hard particles or ceramics serve as reinforcement. MMCs are used to improve the functionality of a wide range of technical materials. It could be used in many different fields, including aerospace, automotive, space travel, and medicine. In this paper, the reviewer investigates the distribution of reinforcement and Tensile Strength (TS) of Aluminum Lithium (Al-Li) Alloy/Nano Al2O3 MMC fabricated by stir casting. Finally, the authors provide a comparative analysis of prior reviewed research papers. After comparative analysis, TiB2/2195 composite has higher Tensile Strength (115.4%) than the other composite such as AA7010-TiB2 (260%), Al2O3 + SiC (72%), A356/SiC (21.87%), and Al-SiC (37%).

Effect of Short-Fiber Orientation on the Tensile Strength of Epoxy Adhesives

Short-glass-fiber-reinforced adhesives are state-of-the-art materials used in the bond lines of wind turbine blades. Various alignments of the short fibers are emerging, which depend on the adhesive flow during the application and joining processes. This induces a spectrum of direction-dependent mechanical properties. The tensile strength, for instance, can vary by about 20% depending on the load direction. Therefore, the adhesive performance, which is normally determined under controlled laboratory conditions and implemented in bond line design routines, can deviate from the in situ application. This work investigates the effect of the short-fiber alignment on the tensile strength distribution of an industry-standard adhesive used in wind turbine rotor blades. The smeared short-fiber orientation of the tensile specimens tested is estimated locally near the damaged surface using a material model that is fed with thermomechanical measurements and calibrated via micro-computed-tomography analysis. A linear correlation between tensile strength and short-fiber alignment has been identified. This augments the identification of the material’s upper and lower strength limits for bond line design purposes.

Evaluation of the tensile strength of Korean yellow poplar lumber

This study was conducted to confirm the feasibility of using yellow poplar, which is a fast-growing hardwood species in Korea, as a structural material. Lumber was produced, and the mechanical grading and the knot diameter ratio on the wide surface measurement were performed for each grade of lumber. It was confirmed that the majority mechanical grades of yellow poplar were E10, E11, and E12, and the size of knot in the surface increased as the mechanical grades decreased. A fitted distribution of tensile strength of the lumbers was the Weibull distribution. As a result of calculating the tensile allowable stress using the 5th percentile value calculated by the Weibull distribution and the non-parametric method according to the mechanical grade, all the experimental values were higher than the minimum allowable stresses presented in the Korean industrial standards. However, for the low grades, there was no significant difference from the standard values. This was thought to be due to the large size of knots in low-grade lumber. It was expected that the prospect of using yellow poplar structural member will be higher if additional research is conducted on the restriction of knot size according to the mechanical grade.

Tensile Force Distribution And Development Within Geogrid-Reinforced Retaining Wall

Abstract Geogrid-reinforced earth retaining walls used to improve soil quality, and provide additional shear strength in the soil mass through the tensile strength in the reinforcement layers. A numerical model was developed by finite element code PLAXIS2D, of a segmental facing geogrid-reinforced retaining wall. This research has been carried out to investigate the effect of loading increments, loading increments width, loading increments location, facing inclination angle, geogrid inclination angle, and geogrid-soil friction factor, on the behaviour of a geogrid-reinforced soil retaining wall. The results show that the failure plane occurred in the reinforced zone at the mid-height, this observation contradicted the triangular distribution with depth assumed in conception methodologies for reinforced soil retaining wall. The distribution of peak tensile strength with depth was bilinear at high loading increments and became trapezoidal at low loading ones. Furthermore, it was found that the behaviour of a geogrid-reinforced soil retaining wall is independent of loading increments width beyond 0.5H. It also seems that the loading increments location can change the shape and the position of the peak tensile strength. It also seems that the geogrid inclination angle has a major effect on the lateral facing displacements and safety factor.

Tensile strength degradations of mineral grain interfaces (MGIs) of granite after thermo-hydro-mechanical (THM) treatment

Granite for hosting the deep geological repository (DGR) is subjected to thermo-hydro-mechanical (THM) treatment for decades of years, while the variations in the tensile strengths of mineral grain interfaces (MGIs) with THM treatment are still unknown. Served as an important parameter in determining the macro mechanical properties of granite, quantifying the tensile strength degradation of MGI with THM treatment is crucial for ensuring the long-term safety of DGR. In this study, the varied tensile strengths of MGIs in the granite after different THM treatments were first directly measured based on a self-developed single-MGI mechanical test system. Three-bending tests were conducted on six-hundred MGIs, which were submitted to various THM treatments with a temperature of 25–175 °C and a pore pressure of 0–15 MPa. The tensile strengths of the interfaces of quartz, feldspar and the interfaces between quartz and feldspar were derived based on the Dugdale–Barenblatt (D–B) model. Results show that the average tensile strength of the interfaces of quartz is 1.06 times larger than that of interfaces between quartz and feldspar, and 1.13 times larger than that of the interfaces of feldspar. Besides, the tensile strength of MGIs seems more susceptible to the pore pressure than to the temperature, and the degradation of tensile strength is the most obvious in the interfaces between quartz and feldspar, followed by the interfaces of feldspar and finally the interfaces of quartz after THM treatments. Based on the characteristics of the tensile strength distributions of different MGIs after THM treatments, the tensile strength degradation models of MGIs related to THM treatments were proposed in meso scale.

Tensile strength and crack tip stress distribution of modified glass in the composite laser beam separation

The tensile strength of the modified cross-section (MCS) determines to a certain extent whether the composite laser can complete the separation of glass, and the quality and efficiency of the separation. In this work, the effect of the picosecond Bessel laser on the tensile strength of soda-lime glass was systematically investigated for the first time. The relationship between the tensile strength and residual stress was not negatively correlated absolutely. The tensile strength was also related to the homogeneity and micro-structure of MCS, including micro cavities, cracks, and voids. Meanwhile, it was pointed out that by selecting appropriate modified parameters, the plasma shielding effect can be suppressed and the micro-morphology of MCS can be controlled to obtain smaller tensile strength and better cutting quality. Secondly, the stress field distribution at the crack tip was simulated to analyze the mechanism when the continuous wave (CW) laser interacted with the modified glass. The simulation results showed that only the stress perpendicular to the laser incidence direction and the scanning direction exceeded the tensile strength of glass material, ensuring that the cracks propagated only along the MCS. Finally, one-time separation of glass was achieved by using a composite laser beam separation (CLBS) technology with a speed of 50 mm/s, which was comparable to the industrial level, and the roughness of separated sidewall was less than 0.5 μm.

The Experimental Study on the Mechanical Properties of Fiber-Reinforced Metal Laminates Using an Innovative Heat-Solid Integrated Forming Technology

In the forming process of fiber-reinforced metal laminates (FMLs) product, the exploratory compound forming technology, including hot stamping of aluminum alloy and laying process of fiber prepreg which is named HFQ-FMLs was proposed to solve the puzzles such as weak rigidity, low strength and integration deformation with large difficulty, and the feasibility and mechanical properties of the innovative forming process were studied. Firstly, based on the modified metal volume fraction formula, the theoretical values of the mechanical properties of the HFQ-FMLs plates were calculated. Compared with the experimental results, the minimum error is 1%, proving that the HFQ-FMLs technology scheme is feasible. Secondly, three kinds of metal sheets with different heat treatments and specimens by HFQ-FMLs were carried out for the tensile tests, the mechanical properties distributions were demonstrated, and the influence regularity of the strain rate and rolling direction on the stress analysis was considered at the same time. As can be seen from the distribution of yield strength and tensile strength, the yield stress of metal sheets obtained by HFQ-FMLs technology along the 45° is superior to the raw material and can increase by 46% under strain rate = 0.01 s−1. While, because the vacuum thermal curing treatment makes the aluminum alloy happen double aging, the metal sheet strength dropped, and the jointing strength between the metal and fiber prepreg became weak too, which made the strength limit of the new material improve weakly. Thirdly, the fractured style of the FMLs under different conditions was studied qualitatively. It is helpful to achieve the development rule of defects, optimize the craft route, and avoid deformation failure.

Mechanical and Surface Geometric Properties of Reinforcing Bars and Their Significance for the Development of Near-Surface Notch Stresses

Due to the production process, reinforcing steel bars possess an inhomogeneous microstructure associated with different material properties over the cross-section (e.g., hardness, ductility or strength). Furthermore, the surface required for the bond has a negative effect on the fatigue behavior. The first investigations were carried out in the 1970s and detected the fillet radius r as a key influencing factor. Until now, few studies had been carried out that investigate the quantification of the surface properties on the fatigue behavior, and none of them compared these properties with the local strengths of the material. The current paper presents the first results of a reverse-engineered reinforcing steel bar based on a previously performed laser scanning process. The rebar models were used to calculate the notch stress factors for different diameters based on von Mises stresses taken from FEM simulations. The notch stress factors showed a functional relationship with the fillet radius, which was already shown in the literature. Further experimental investigations on the fatigue and tensile behavior of the structural components in the investigated Tempcore® rebars were carried out on microstructure specimens eroded by WEDM. The results of the tensile tests were used to derive a yield and tensile strength distribution in the cross-section. Depending on the microstructure, a yield strength between 415 N/mm2 (ferrite/pearlite core) and 690 N/mm2 (tempered martensite surface) was found. The acting notch stresses show a logarithmic dependency of the fillet radius, but do not reach the material strength of the surface.

Multi-objective optimization of mechanical and microstructural characteristics in a stir casting process of MWCNTs/Al6082 composites using neutrosophic TOPSIS and GRA

ABSTRACT The objective of this paper is to find optimum process parameters of stir casting process for multi-walled carbon nanotubes (MWCNTs) reinforced Al6082 composites in a multi-objective optimization context. In this work, output parameters include ultimate tensile strength (UTS), hardness, compressive strength (CS), and uniform distribution of MWCNTs. Among these, first three parameters can be measured, and data can be obtained in quantitative terms. However, uniformity of distribution of MWCNT is a qualitative variable, and hence neutrosophic sets are used in this work. Each of the four input process parameters, such as fraction weight of MWCNTs, stirring speed, furnace temperature, and stirring time, are taken at three levels each, and experiments are designed using Taguchi L27 array. Information entropy method is used to compute the weights of output parameters. TOPSIS method is used to normalize the quantitative data, and neutrosophic TOPSIS is applied for normalizing the data related to uniformity. It is found that MWCNT’s percentage of 0.9, speed of 450 rpm, temperature of 800°C, and time of 10 minutes, yield best output parameters. Neutrosophic gray relational analysis is also used to find optimum solution for above case, and the optimum values obtained from both methods are compared.

Hierarchical scaling model for size effect on tensile strength of polycrystalline rock

Here, we proposed an analytical model for quantifying the intriguing size-dependent tensile strength of polycrystalline rock, i.e. first ascending then descending with the increase of specimen size. The meso‑structure of polycrystalline rock was firstly degraded to a hierarchical arrangement of regularly cuboid mineral grains. The tensile strength distribution of mineral grain interface (GI) is modeled by Weibull distribution, and the stress state near the failed GI is analytically calculated. Then a probabilistic analysis of the failure evolution in hierarchical mineral grain sets (sets of sets) was performed by considering the meso crack initiation at the GI to their propagation at macro scale, so that the tensile strength distribution and the meso crack accumulation in the rock specimen can be derived. The consistency between the model predictions and experimental results demonstrates the proposed model is valid. In addition, the results revel that the size effect trend, ascending or descending, is determined by the dispersion degree of structure strength distribution.

Experimental determination of bimodal strength distribution of S-glass fibers

Tensile strength distribution of S-Glass fibers at small gage lengths on the order of the ineffective length is required for both analytical and numerical models of composite unidirectional tensile strength. Historically unimodal Weibull strength distributions measured at large gage lengths are extrapolated to smaller length scales (5–200 μm). The accuracy of this approach is assessed by using 2 different experiments – the filament tensile test (gage lengths > 4 mm) and a continuously-monitored Single Fiber Fragmentation Test (SFFT, gage length = 544 μm). Extrapolation of the unimodal Weibull distribution to the 544 μm gage length leads to significant overprediction of fiber strengths (by ∼60%). The Weibull distribution obtained from SFFT also shows a significantly higher Weibull Modulus (12.9) as opposed to the tension dataset (4.5). This indicates that a different population of defects dominate at the shorter gage lengths. A bimodal Weibull equation has been fit to the combined data to account for the 2 different defect populations to provide accurate strength predictions over fiber lengths from ∼500 μm to 30 mm. An independent validation experiment was performed at 2 mm gage length to validate the Bimodal Equation.

Design and development of auxetic structures for enhancing ergonomic comfort in women’s intimate apparel (brassiere)

Brassiere straps are commonly perceived as one of the most irritating and uncomfortable components of a brassiere, especially for women with heavier breasts. This study aimed to design and developed auxetic structures to enhance the ergonomics of intimate apparel. The brassiere straps were developed by using textured polyester and nylon yarns with auxetic weave structures in two different widths. Tests were conducted to evaluate Poisson’s ratio, tensile strength, and pressure distribution properties and overall ergonomics of developed straps. Subjective analysis was also performed by conducting wear trials. The development of polyester straps yielded excellent results compared to nylon. In the subjective analysis, the selected polyester sample consistently performed better than others, significantly enhancing ergonomics comfort, fit, and psychological comfort according to respondents’ preferences. Based on the results, Auxetic structure can be a better alternative for brassiere straps in active wear to avoid related health problems and to improve women’s experience.

Influence of Process Parameters and Particle Size Distribution on Mechanical Properties of Tablets

AbstractThe influence of the particle size distribution of maltodextrin powders with a dextrose equivalent level of 29 as well as two tableting process variables, namely the compression pressure and the dwell time, on the tensile strength, porosity, and pore size distribution of the final tablet was studied. The mechanical strength and porosity of the tablets are assessed in relation to the powder and process parameters. Regarding the process parameter, it was show that the compaction pressure clearly has a more pronounced influence on the tablet porosity and mechanical strength compared to the influence of the dwell time in the range of the study. As a result, the study offers a better understanding of how the properties of a tablet are influenced by the inter‐correlation of powder characteristics and tableting parameters. Therefore, the shelf‐life studies and tablet downstream processing as well as drug product development will benefit greatly from this work.

Research on the micro zone strength and strain hardening behavior in the 30Cr2Ni4MoV rotor welded joint

In order to investigate the micro zone tensile properties of a 30Cr2Ni4MoV rotor welded joint used for an ultra-supercritical steam turbine, a thin plate tensile test method is put forward by taking the micro zone size into account. The microstructures of welded joint are observed by OM, SEM and TEM, and a strength prediction model based on the microhardness and the strain hardening exponent is established. The researches show that the weld metal (WM) has lower strength than the base metal (BM), but similar plasticity and strain hardening ability, that the heat affected zone (HAZ) has a sharp distribution of tensile strength due to the great changes in grain size and microstructure. Based on the hardening rate analysis with Kocks-Mecking (K-M) model, the coarse-grained HAZ (CGHAZ) only experienced two strain hardening stages Ⅲ and Ⅳ, and other micro zones of the welded joint exhibited three strain hardening stages Ⅲ, IV and Ⅴ. The coarse tempered martensite in CGHAZ has poor coordination deformation ability, resulting in its short strain hardening stage IV. More tempered bainite and finer tempered martensite are beneficial to extending the strain hardening period. By observing the microstructures after tensile tests, it is found that the dislocation cells formed more uniformly in the tempered bainite than in the tempered martensite, and only the intragranular carbides have a beneficial effect on the strain hardening behavior. An equation for predicting the micro zone strength is established, and the micro zone strength distribution along the welded joint is successfully predicted.

Platelet-Rich Fibrin Progressive Protocol: Third Generation of Blood Concentrates

Platelet-rich fibrin (PRF) has been used in several fields of dentistry to improve tissue healing. However, PRF from glass tubes results in a limited number of small membranes, increasing clinical difficulty and work time. The aim of this study was to evaluate cell and platelet amounts and biomechanical strength of PRF-giant membranes produced from plastic tubes without additives. The investigators designed an exvivo study, to compare 3 different centrifugation protocols for obtaining PRF: 700×g/12minutes (leukocyte and PRF [L-PRF]), 350×g/14minutes (GM350), and 60-700×g more than 15minutes total (progressive PRF [PRO-PRF]). We collected blood samples from 5 volunteers aged 25-54years, over 3 different time periods (triplicate and paired study). From each venipuncture, 4mL of blood was collected in vacutainers with ethylenediamine tetraacetic acid (EDTA) and approximately 104mL in 12 plastic tubes without additives, which were separated into 3 groups, as per the centrifugation protocols (n=5): L-PRF, GM350, and PRO-PRF. The PRF from the tubes of the same protocol was aspirated and 9mL were placed in polylactic acid (PLA) forms and 3mL were placed in a glass receptacle. The membranes from PLA forms were tested for tensile strength and the membranes from glass receptacles were evaluated by histomorphometry, while platelets and leukocytes were counted for those in tubes with EDTA. Statistical analyses were performed using Shapiro-Wilk normality test and then a one-way repeated measures analysis followed by Tukey multiple comparisons test (α<0.05). In tensile analyses, PRO-PRF (0.85±0.23N) showed a significantly higher maximum breaking strength than L-PRF (0.61±0.26N, P=.01) and GM350 (0.58±0.23N, P<.01). The histomorphometry revealed no significant statistical difference in cell counts between the groups (P=.52). Furthermore, there was no significant difference between the leukocyte (P=.25) and platelet counts (P=.59) in whole blood between the groups. The progressive protocol (PRO-PRF) enabled the production of PRF giant membranes with greater tensile strength and adequate cell distribution. Moreover, it allows biomaterial incorporation during production and enables clinical control of membrane thickness and size as per the surgical procedure.

A Three-Parameter Weibull Distribution Method to Determine the Fracture Property of PMMA Bone Cement.

Poly (methyl methacrylate) (PMMA) bone cement is an excellent biological material for anchoring joint replacements. Tensile strength and fracture toughness have a considerable impact on its application and service life. Considering the variability of PMMA bone cement, a three-parameter Weibull distribution method is suggested in the current study to evaluate its tensile strength and fracture toughness distribution. The coefficients of variation for tensile strength and fracture toughness were the minimum when the characteristic crack of PMMA bone cement was . Using the simple equation and fictitious crack length , the mean value (= 43.23 ), minimum value (= 26.29 ), standard deviation (= 6.42 ) of tensile strength, and these values of fracture toughness ( = 1.77 , = 1.02 , = 0.2644 ) were determined simultaneously through experimental data from a wedge splitting test. Based on the statistical analysis, the prediction line between peak load and equivalent area was obtained with 95% reliability. Nearly all experimental data are located within the scope of a 95% confidence interval. Furthermore, relationships were established between tensile strength, fracture toughness, and peak load . Consequently, it was revealed that peak load might be used to easily obtain PMMA bone cement fracture characteristics. Finally, the critical geometric dimension value of the PMMA bone cement sample with a linear elastic fracture was estimated.

Softening behavior of stationary shoulder friction stir welded joint for thick-plate Al–Li–Cu alloy

12-mm-thick Al–Li–Cu alloy plates were fabricated by stationary shoulder friction stir welding (SSFSW) to evaluate the softening behavior of the whole joint under a given rotational speed of 400 rpm and a welding speed of 60 mm/min. Continuous dynamic recrystallization, discontinuous dynamic recrystallization, and geometric dynamic recrystallization are the main dynamic recrystallization mechanisms in SSFSWed joints. Such mechanisms help to gradually change rolling grains of base material (BM) into equiaxed grains of welding nugget zone (WNZ) and significantly lower dislocation density. The decrease in dislocation density is the main reason for joint softening. Continuous coarsening of T1/θ′ in heat affected zone (HAZ) and thermo-mechanically affected zone (TMAZ) weakens the strengthening effect. The development of precipitate-free zones and re-precipitation of TB primarily contribute to severe softening at the interface between HAZ and TMAZ on the advancing side (AS-HAZ-TMAZ). The serious softening behavior at the bottom of WNZ is attributed to the re-precipitation of TB and the complete dissolution of T1/θ′. Hardness profiles and tensile strength distribution of SSFSWed joint exhibit a “W” pattern, while a “U” pattern appears at the bottom. The hardness profile and tensile strength of WNZ are significantly poorer at 8–12 mm from the weld surface compared to those at 0–8 mm. Softening behavior also results from the higher fractions of the maximum Schmid factor (in 0.4–0.5) and Cube. From BM to WNZ, fracture mode transitions from quasi-cleavage fracture to plastic fracture.