Representative Stress-strain Curves Research Articles

Triaxial experimental study of mechanical behavior of non-persistent jointed granite subjected to slight cyclic dynamic disturbances

A slight disturbance can induce fault-slip burst failure in deep rock masses. In this paper, a series of triaxial tests were conducted to investigate the strength, deformation characteristics, and failure behavior of non-persistent jointed granite specimens subjected to slight cyclic loading. A representative stress–strain curve for non-persistent jointed rock was generated and used to study the crack evolution process (initiation → propagation → coalescence). The effects of varying the joint angle and frequency and amplitude of the disturbance were then analyzed. A theoretical (fracture mechanics) model for a non-persistent joint subject to triaxial cyclic loading was also established and used to investigate the combined effects of static confining stress and slight disturbances. Finally, the mechanical mechanism by which a slight dynamic disturbance induces fault-slip burst was discussed. Our results show that the failure mode of a non-persistent jointed rock mass depends more on the joint angle than the amplitude and frequency of the slight disturbance. The disturbance induces the initiation and extension of cracks. It can also induce fracture-slip bursting once the disturbance exceeds a certain threshold. The value of this threshold depends on the initial stress state, joint angle, length, dynamic and static friction coefficients, and fracture toughness of the rock. The study thus enriches our mechanistic understanding of the crucial ingredients involved in the triggering of fault-slip rock bursts in deep rock masses by slight disturbances.

Development of a Lytag-silica fume based lightweight concrete and corresponding design equation for pure bending

This study presents a novel Lytag-silica fume concrete (LSFC) for structural and other construction applications. The evaluation of compressive strength development and stress strain relationships of the LSFC light weight was carried out to determine the strength growth in LSFC and for the development of the proposed beam design equation. Four different mix compositions were adopted for concrete grade 20, 30, 40, 50 at cement dosage of 260, 330, 450 and 570 kg/m3 on 24 concrete samples. A rectangular parabolic stress block was derived using representative stress-strain curves, and the results show that the parameter kbal that defines the ultimate design moment in the compressive zone was equal to 0.107 compared to kbal value of 0.167 for a normal weight concrete according to Eurocode 2. The ultimate compressive strain obtained for LSFC was 2.18‰ after 28 days for the LSFC compared to that of the normal weight concrete (NWC) of 3.5‰. The result also shows that 94.15 % of the compressive strength of LSFC was developed within 7 days of age due to the high pozzolanic chemical composition of Lytag and Silica fume. A reduction in embodied carbon was evident on reduction in water to cement ratio. The analysis and design results compared with NWC shows that Lytag-silica fume light weight concrete reduces reinforcement to 47 % with an increase in shear resistance. Scanning Electron microscopy analysis shows that the pathology and microstructure of the lytag-silica fume concrete is characterised with high micro pores with increasing water to cement ratio while the low water to cement ratio exhibit low distribution of pores which is an attribute of good mechanical properties of LSFC. The stress strain behaviour does not display a strain softening phenomena which is indicative of good flexural strength.

Experimental and analytical study of hollow section concrete-filled GFRP tubes in bending

The flexural response of hollow section concrete-filled GFRP tubular (HS-CFGT) members has been examined experimentally and reported in this paper. A total of 14 specimens was tested, including four-point bending tests on reduced-scale specimens in the laboratory and cantilever bending tests on full-scale specimens on the construction site. The details of the test rigs and procedures, as well as the key test observations, including the ultimate moment capacities, load–displacement curves and failure modes, are fully reported. The test results were analysed to evaluate the influence of key variables on the structural performance of the HS-CFGT tubes, including concrete infill, GFRP tubes, slips between concrete and GFRP tubes and confinement of concrete infill. Fibre analysis approach was adopted to determine the moment capacity of the examined HS-CFGT sections. A total of four representative stress–strain curves of concrete were evaluated for their applicability to the HS-CFGT sections in bending. It was found that the concrete models proposed for general FRP-confined concrete columns are not applicable to the examined HS-CFGT sections in bending, and the uniaxial concrete model leads to rather conservative moment predictions, whereas, the FRP-confined concrete model used for beams provides great accuracy in predicting the moment capacities for both reduced-scale and full-scale HS-CFGT members.

Compressive impact tests of lightweight concrete with 155-mm-diameter spilt hopkinson pressure bar

High-strength, lightweight concrete materials have been widely used in many building structures, while the dynamic behaviors under high-strain-rate loading are not well understood. Two groups of high-strength, lightweight concrete specimens were cast for static and dynamic tests. The compressive strengths and densities of the specimens were 39.6 N/mm2 and 1.3 t/m3, respectively. Specimens with length-to-diameter ratios of 0.5 and 150-mm-diameter were tested using a 155-mm-diameter split Hopkinson pressure bar (SHPB). A copper disc was applied as the pulse shaper, and the resulting impact velocity was proven to be stable in each test scenario. The damage mode of the concrete specimens was brittle failure, and fragments with different sizes were generated after each impact. The higher the impact velocity was, the smaller the sizes of the fragments became. A representative stress–strain curve was developed based on the geometric shape of the observed curve for each specimen. The dynamic strength generally increased with the impact velocity for strain rates ranging from 40 to 140 s−1. A new profile consisting of one parabola and two straight lines was developed to represent the experimental dynamic increase factor. The energy absorption density and fragility curves were computed to understand the energy absorption and fragility properties of the specimens.

Vertical Fibrous Morphology and Structure-Function Relationship in Natural and Biomimetic Suction-Based Adhesion Discs

Summary Recent years have seen rapid development in bio-inspired materials for adhesion. However, it remains challenging to realize robust adhesion on rough aquatic surfaces. An inspiring natural model is the remora fish, which has evolved to retain powerful adhesion to hosts using a dorsal suction disc. We find that the remora suction disc has a unique fibrous architecture of vertically oriented collagen fibers that enable anisotropic mechanical properties and enhanced adhesion performance. In the engineered prototype, vertically oriented nylon fibers are embedded into the soft silicone matrix using electrostatic flocking. The anisotropic mechanical properties are validated in both natural and biomimetic suction discs. Furthermore, the biomimetic suction disc demonstrates an enhanced adhesion function with a maximum 62.5% increase in pull-off force and a 340% increase in attachment time compared with the silicone control. This work can shed light on natural adhesion mechanisms and inspire novel designs for aquatic soft adhesives and actuators.

Corrigendum to “Representative Stress-Strain Curve by Spherical Indentation on Elastic-Plastic Materials”

Corrigendum to “Representative Stress-Strain Curve by Spherical Indentation on Elastic-Plastic Materials”

Characterization on stress-strain behavior of ferrite and austenite in a 2205 duplex stainless steel based on nanoindentation and finite element method

Abstract The stress-strain behavior of ferrite and austenite in a commercial 2205 duplex stainless steel was investigated by using nanoindentation test and microstructure-based finite element method (FEM). Results showed that the optimum load range for measuring phase properties in nanoindentation test was from 3000 μN to 7000 μN. The ferrite has slightly higher average elastic modulus than austenite, while austenite has higher average nanohardness than ferrite. Representative stress-strain curves of ferrite and austenite were determined by means of the power-law hardening and empirical relationship. Based on FEM, the differences in distribution and portion of stress-strain in local phases were visualized, and the overall flow curve of the sample 2205 was extracted, which was in good agreement with the obtained results from uniaxial tensile experiment.

Dynamic Characteristics of Green Sandstone Subjected to Repetitive Impact Loading: Phenomena and Mechanisms

A split Hopkinson pressure bar apparatus driven by a pendulum hammer was used to perform uniaxial compression tests to examine the degradation process of green sandstone subjected to repetitive impact loading. The acoustic characteristics, dissipated energy, deformation characteristics, and microstructure evolution were investigated. The representative stress–strain curve can be broken into five stages that were characterized by changes in the axial strain response during impact loading. Both the ultrasonic wave velocity and cumulative dissipated energy exhibited obvious three-stage behavior with respect to the impact number. As the impact number increased, more than one peak was observed in the frequency spectra, and the relative weight of the peak frequency increased in the low-frequency range. According to the evolution of the ultrasonic wave velocity, the degradation process was divided into three stages. By comparing the intact stage I and early stage II microcrack development patterns, the initiation of new cracks and elongation of existing cracks were identified as the main degradation mechanisms. Furthermore, a slight increase in the number of cracks was observed, and microcrack lengths steadily increased. Moreover, due to the low level of microcrack damage, the deformation mechanism was mainly characterized by volume compression during impact loading. In late stage II, the main degradation mechanism was the elongation of existing cracks. Additionally, as microcracks accumulated in the rock samples, cracks were arranged parallel to the loading direction, which led to volume dilation. In stage III, microcracks continued to elongate nearly parallel to the loading direction and then linked to each other, which led to intense degradation in the rock samples. In this stage, rock sample deformation was mainly characterized by volume dilation during impact loading. Finally, rock samples were split into blocks with fractures oriented subparallel to the loading direction. These results can improve the understanding of the stability evaluations of rock structures subjected to repetitive impact loading.

A scaling law for predicting the ballistic limit of aluminium alloy targets perforated in ductile hole formation

The ballistic performance of monolithic targets perforated in ductile formation by rigid projectiles can be reasonably approximated by an energy balance based on the work done in expanding a hole from zero initial radius to that of the penetrating projectile. For a specific projectile, these energy balance laws can be expressed in terms of a simple scaling law which requires an empirical fit to ballistic data. However, once this fit has been performed for a specific projectile against a specific target material, predicting the performance of other materials against this projectile can be done from a simple quasi-static compression stress–strain curve, provided the target is perforated in ductile hole formation. Four variations of ductile hole formation analytical and semi-empirical models have been reformulated as scaling laws and evaluated for their ability to characterise the performance of monolithic aluminium plates impacted by 7.62 mm APM2 projectiles at normal incidence. The database used to fit and evaluate the performance of the scaling laws incorporates more than 1600 V50 measurements against 24 different alloys and tempering/strain-hardening combinations with thicknesses ranging from 16.2 to 63.5 mm. The highest performing scaling law formulation was found to characterize the measured V50 to within 5% of the experimental value for over 97% of the database entries. Further improvements in accuracy are likely impossible when representative stress–strain curves are used for performance characterization rather than tests of each individual plate used in the ballistic tests. The scaling law can be applied to predict the performance of targets perforated in ductile hole formation with a high level of confidence, an example of which is provided for the 12.7 mm APM2 projectile against a range of aluminium alloys.

A practical note for SHPB test with new algorithms for delimiting pulses

Data processing in split Hopkinson pressure bar technique is known to be sensitive to limits and durations of the incident, reflected and transmitted strain pulses. The dynamic stress–strain curves were found to be affected by dispersion and shifting of elastic strain pulses traveling the elastic bars. In this study, a practical note was given for split Hopkinson pressure bar test with describing new iterative algorithms that we developed for delimiting SHPB strain pulses. The developed algorithms were validated through typical in-plane dynamic compressive loading tests on [±55°]20 E-Glass/Epoxy aged laminates tested in the range of 560–1025s−1. Representative stress–strain curves were reported in this paper. The strain rate was found to be linearly pressure dependent. The dynamic modulus was found to be strain rate dependent however there was a threshold effect for the ultimate strength and strain at ultimate strength. Failure mechanisms were characterized through optical and scanning microscopy. Data for dynamic properties were fitted in empirical models.

D-36 Free Communication/Poster - Ultrasound

PURPOSE: The molecular mechanism of bone strengthening with exercise remains unclear. We have identified a molecule, follistatin-like 3 (FSTL3), that may drive mechanical load-dependent bone remodeling. METHODS: Female Sprague Dawley rats (12-14 wks, n=10), wild-type (Fstl3+/+, 10-12 wks, n=10) or homozygous Fstl3-/- C57Bl/6 mice (10-12 wks, n=10) were subjected to treadmill walking (EX) for 45 min/day. After 0, 2, 5 or 15 days of EX, gene expression was analyzed by quantitative real time polymerase chain reaction, Western blots, or immunohistochemistry of the trabecular bone/bone marrow at distal femur ends. Bone mineral apposition rates were assessed by administration of Calcein and Alizarin complexones on day 3 and 12. Statistical analysis was performed by one-way ANOVA with Tukey’s post hoc or T-test. RESULTS: Gene expression analysis revealed that EX stimulated Fstl3 mRNA expression by 6 fold on day 2, and mRNA declined to basal levels by day 5. Minimal FSTL3 protein expression was exhibited in the control non-EX trabecular bone, but a robust increase in FSTL3 expression was observed in EX rat femurs at days 2 and 5. Non-EX mice exhibited a significantly narrow distance between the Calcein and Alizarin incorporation and limited bone deposition. EX Fstl3+/+ and Fstl3+/- mice demonstrated a significant increase in bone deposition on the endosteal surface of the femurs not observed in Fstl3-/- mice. Representative stress-strain curves of the cortical bone of the Fstl3+/+ and Fstl3 -/- femurs revealed that strain at ultimate strength of femurs from Fstl3+/+ mice was approximately 25% > than that of Fstl3 -/- mice. Furthermore, the yield strain and yield energy were significantly upregulated by EX in Fstl3+/+, but not in Fstl3-/- mice. CONCLUSION: FSTL3 is a mechanoresponsive protein that may provide a new paradigm for investigating EX-driven bone formation as well as a marker to monitor the effects of EX on bone in health and disease.

Extraction of Plastic Properties of Aluminum Single Crystal Using Berkovich Indentation

An alternative to extract representative stress-strain curves from a set of indentation data measured with the Berkovich indenter is developed in this study. The depth in the representative strain is identified by a double logarithm plot of indentation data, and it enables the establishment of a representative stress-strain curve. Comprehensive analyses are demonstrated using the new method proposed to capture the yield strength and the strain hardening exponent for an aluminum single crystal.

Evaluation of stress–strain curve estimates in dynamic experiments

Accurate measurements of the forces and velocities at the boundaries of a dynamically loaded specimen may be obtained using split Hopkinson pressure bars (SHPB) or other experimental devices. However, the determination of a representative stress–strain curve based on these measurements can be challenging. Due to transient effects, the stress and strain fields are not uniform within the specimen. Several formulas have been proposed in the past to estimate the stress–strain curve from dynamic experiments. Here, we make use of the theoretical solution for the waves in an elastic specimen to evaluate the accuracy of these estimates. It is found that it is important to avoid an artificial time shift in the processing of the experimental data. Moreover, it is concluded that the combination of the output force based stress estimate and the average strain provides the best of the commonly used stress–strain curve estimates in standard SHPB experiments.

Banana Fibers – Variability and Fracture Behaviour

Banana fibers obtained from the stem of banana plant (Musa sapientum) have been characterised for their diameter variability and their mechanical properties, with a stress on fracture morphology. The nature of representative stress strain curves and fracture at different strain rates have been analysed through SEM.

A comparison of the predictive capabilities of current failure theories for composite laminates: additional contributions

Following the publication of an article by Soden, Hinton and Kaddour (Compos Sci Technol, V58, pp. 1225–54, 1998), which compared the predictions of 14 internationally recognised failure theories for fibre reinforced polymer composite laminates, the present paper extends that comparative study to include five more theories, supplied by their originators. Evaluation of the predictive capabilities of the additional theories was carried out in an identical manner to the original study. The same test cases were utilised, covering a wide range of lay-ups, materials and in-plane loading conditions. The results (initial and final failure envelopes and representative stress–strain curves) have been superimposed to show similarities and differences between the predictions of the 19 theories. Final failure predictions for the additional theories fall within the existing range obtained from the original 14 theories but the initial failure predictions for the additional theories have widened the previously observed range. Comments are provided on the possible reasons for the increased spread.

Correlation of Test and FEA Results for the Nonlinear Behavior of Straight Pipes and Elbows

This paper summarizes the literature on reconciliation of finite element analyses with in-plane bending experiments on piping elbows. It then describes in detail two four-point-bending tests on straight pipes and two in-plane bending tests on elbows and the corresponding nonlinear finite element analyses. Using a new procedure for obtaining a stress-strain curve for stainless steel using only values for E,Sy, and Su and a representative stress-strain curve from a test on a similar material specimen, the nonlinear responses of the piping components tested are shown to be simulated more accurately than previously published results.

Three-dimensional periodic Voronoi grain models and micromechanical FE-simulations of a two-phase steel

A three-dimensional model is proposed for modeling of microstructures. The model is based on the finite element method with periodic boundary conditions. The Voronoi algorithm is used to generate the geometrical model, which has a periodic grain structure that follows the original boundaries of the Voronoi cells. As an application, the model is used to model a two-phase ferrite/pearlite steel. It is shown that periodic cells with only five grains generate representative stress–strain curves.

Mechanical Testing of Free-Standing Thin Films

AbstractAn overview is given of methods for testing thin-film tensile specimens of either MEMS materials or surface coatings. MEMS specimens are deposited in a final shape and need only to be released for testing, while specimens of coating materials must be extracted. Very brief descriptions of the specimen designs, force application approaches, and strain measurements are given along with a limited number of references. Representative stress-strain curves for polysilicon, silicon nitride, silicon carbide, electroplated nickel and diffusion aluminide bond coating are presented. Results at high temperatures are presented for the latter two materials.

Mechanical Testing of Free-Standing Thin Films

AbstractAn overview is given of methods for testing thin-film tensile specimens of either MEMS materials or surface coatings. MEMS specimens are deposited in a final shape and need only to be released for testing, while specimens of coating materials must be extracted. Very brief descriptions of the specimen designs, force application approaches, and strain measurements are given along with a limited number of references. Representative stress-strain curves for polysilicon, silicon nitride, silicon carbide, electroplated nickel and diffusion aluminide bond coating are presented. Results at high temperatures are presented for the latter two materials.

ON THE USE OF CONSTITUTIVE INTERNAL VARIABLE EQUATIONS FOR THERMAL STRESS PREDICTIONS IN ALUMINUM CASTING

The report discusses the use of constitutive equations with internal variables in mathematical calculations of the thermally induced strains and stresses that arise during casting of aluminum. Application of the so-called MATMOD (MATerials MODel) constitutive relations for the viscoplastic deformation of the material is first discussed in relation to the specific characteristics of the casting process. Some numerical time integrations of the one-dimensional version of the MATMOD equations that are relevant for aluminum casting are then presented. The evolution of temperature and total strain are here chosen to be close to values experienced in the direct chill (D.C.) casting process, and values for thermally induced strains and stresses are calculated. The results are compared with predictions based on the traditional approach, in which a set of representative stress-strain curves at different constant temperatures and strain rates constitute the complete description of the viscoplastic deformation.