straincurve correction. Tang and Lee  analyzed necking in a bar under simple tension using a coupled strain hardened and damage models. He studied the effect of damage model on the necking phenomenon. Since necking is inherently a consequence of damage (void growth and coalescence), coupling of material model with damage model can significantly improve the correction techniques. Ling  introduced a special function for describing the relation between stress and strain after necking. He obtained the function by numerical simulation using Abaqus. His analysis was based on optimization of the difference between experimental and numerical load-displacement curves. A number of creative correction techniques have been proposed by researchers such as Mirone . His method is applicable to a wide range of metals. Mirone  presented some criteria independent of the type of material and introduced relations for stress-strain correction. Coppieters et al.  presented an alternative method to identify the post-necking hardening behavior of sheet metal. His method is based on the minimization of the difference between the internal and external work in the necking zone during a tensile test. Eduardo  presented an experimental- numerical methodology to derive the elastic and hardening parameters which characterize the material response. Yang and Cheng  introduced a damage mechanics based model to describe the progressive deterioration of materials prior to initiation of macro cracks. Majzoobi et al. [17, 18] identified the constants of Johnson–Cook, power law and Zerilli–Armstrong models in tension and compression using a combined experimental/ numerical/ optimization approach. The models take account of correction indirectly and there is no need for computing the correction factor directly. Gromada et al.  analyzed and estimated the accuracy of the well-known classical formulae for correction stress-straincurve.
Masaharu et al.  discussed the effects of shape and volume fraction of a second phase on stress states and deformation behavior of two-phase materials with the help of empirical relations. They embedded inhomoge- neous spheroidal (second phase) inclusions in a matrix. Analytical expressions to describe the stress states in elastically and plastically deformed two-phase materials are obtained with the Eshelby method and the Mori- Tanaka concept of the “average stress”. Considering that the second phase is also plastically deformable, the over- all deformation behavior of the two-phase materials is discussed with the results obtained by the evaluation of the stress and strain distributions in the materials. Some of the authors predicted the stressstraincurve with the help of empirical relations [25-28] and phase transfor- mations of titanium alloys [29,30].
In order to predict the nominal stress-straincurve of an isotropic polycrystal Ti-15V-3Al-3Cr-3Sn (hereafter, Ti-15-3(ST)) sheet in tension test, three-dimensional ﬁnite element (FE) analysis is elucidated considering three boundary conditions. According to the constraint at both ends of specimen, three boundary conditions are a simulated case based on the empirical data, a full case and a free case. In the simulated case, the nominal stress-straincurve can be well predicted until the fracture strain. Maximum load point does not mean the termination of uniform deformation in the present study. The onset of localized necking is intensively discussed and the origin of localized necking is concluded to be not due to the plastic instability but due to the deformation constraint at both ends of specimen. [doi:10.2320/matertrans.M2010033]
condition that the two curves could be ﬁtted by similar functions, the cyclic curve could be deduced by the engineering curve theoretically. Meanwhile, although the stress-straincurve of many metals in the region of uniform plastic deformation could be described by the classical Hollomon equation, the equation might not be absolutely appropriate to describe the engineering stress-straincurve. The engineering stress-straincurve does not give a true indication of the deformation characteristics, because it is based entirely on the original dimensions of the specimen, and these dimensions would change continuously during the tensile test. Actually, the true stress-straincurve 13) presents a larger stress value compared with the engineering curve as the cross-sectional area of the specimen is gradually decreasing.
The loading-unloading-reloading process could affect the tensile deformation of metals with the combined function of stress relaxation and work hardening, which has been reported in multiple experiments. Nevertheless, the effects of different unloading positions and unloading times have not been investigated. In this study, unloading-reloading tests on three materials (AL6061, HSLA and Q195) were conducted. The stress exhibits a rapid rise momentarily upon reloading and stabilizes afterward while the post stress-straincurve deviates up or down from the monotonic tensile curve. The ductility is enhanced by the unloading-reloading process in general. Different unloading positions and unloading times have different degrees of influence on the stretching of these metals. The effect of loading conditions on a medium manganese steel was further studied. The functions to modify the post stress-strain relationship af- ter unloading-reloading were established.
There has been an increasing use of permeable con- crete in the civil engineering and building construc- tion industries in recent years (Offenberg 2008). However its use is currently limited to low trafficked areas such as pavements in car parks and footpaths, largely due to its low strength and stiffness. It is timely to investigate the stress-strain behaviour of permeable concrete to help enable its wider use in more structural applications. An understanding of the complete stress-straincurve of permeable con- crete is essential for rational design, as structural de- signers are unable to take full advantage of the mate- rial with insufficient information about this behaviour.
Stress–straincurve and stress–piezoelectric voltage curve As shown in Fig. 2, the stress (s) was plotted against the piezoelectric voltage (P) and the strain (e) for each loading and unloading process. The figure clearly shows that ini- tially most of the s–e curve became convex, and then the stress was proportional to the strain. That is, the s–e curve was nonlinear at a low proportionality level, and had almost the same shape during both loading and unloading. Subse- quently, the s–P curve was nonlinear, with a maximal point or cusp on the curve, and had almost the same shape during both loading and unloading as did the s–e curve.
It is found that, the engineering stress-strain converted directly from the indentation stress-straincurve of a deep spherical indentation test has an agreement with effective stress-strain value defined by equations (11) and (12). The stress and strain constraint factor have empirical values according to Taber's theory and depended on material properties as shown in Table (1) above (Baoxing Xu et al. 2010).
The shape of a load-displacement curve or a nominal stress-straincurve also changes according to deformation method such as tension, compression and bend even if the same ductile metal with an identical true stress-strain relation is considered. 10) In other words, boundary condition deﬁ- nitely aﬀects the shape of the nominal stress-straincurve. Finite element (FE) analysis has been successful in simulat- ing and assessing the plastic deformation behavior for metal forming and also widely accepted as a powerful tool to
Gandhi and Raval  developed the analytical model to estimate the top roller position as a function of desired curvature, for multiple pass three-roller forming cylinders. Gandhi and Raval  proposed that the developed analytical model for the range of the range of the machine setting parameters such as top roller position and center distance between bottom rollers, work should be extend to check the validity of developed model at different material property parameters, machine specifications and plate dimensions. Zemin Fu  an analytical model and finite element model are proposed for investigating the three rollers bending forming process. A reasonably accurate relationship between the down word inner roller displacement and the desired spring back radius of the bent plate is yielded by both analytical and finite element approaches, which all agree well with experiments. Kalyani abhinav  reported that the different sheet metals are considered and different loads are applied and parameters are obtained. From all the condition conclude that the normal stress is maximum only in stainless steel. Total deformation and maximum principal elastic strain is higher for aluminum. Ahmed ktari  proposed that the desired curvature radii were established by varying the distance between the two bottom rollers and the position of the upper one.
The curvilinear stress/strain relationship displayed by this tissue is likely to be related to the way in which its multiple tissue components are integrated. The laminar junction comprises a complex mixture of epidermal, dermal and subcutaneous tissues, collagen and elastin comprising the major structural elements of the soft tissue regions. Collagen orientation in the laminar dermis has not been studied in detail, but Linford (1987) reported predominantly vertical orientation of the collagen fibres in the dorsal part of the foot, proximal to the tip of the third phalanx. The initial low-modulus region of the stress/straincurve reported in this paper is probably dominated by a combination of elastin and the protein–polysaccharide matrix which characterises dermal tissues. These tissue components are not designed primarily for load-bearing, as the low modulus in this region attests. As the collagen network strains and its fibres reorientate, this protein comes to dominate the stress/strain behaviour, giving a higher modulus at higher strains. The stress/strain curves obtained are similar to those previously obtained for skin (Veronda and Westman, 1970). Collagen has a modulus of elasticity in tension of approximately 1 GPa (Wainwright et al. 1976), elastin being three orders of magnitude less stiff, with a tensile modulus of approximately 1 MPa (Dimery et al. 1985) when loaded parallel to the fibres. The value obtained in the
The above discussion is concerned primarily with simple tension, i.e. uniaxial loading that increases the interatomic spacing. However, as long as the loads are suﬃciently small (stresses less than the proportional limit), in many materials the relations outlined above apply equally well if loads are placed so as to put the specimen in compression rather than tension. The expression for deformation and a given load δ = P L/AE applies just as in tension, with negative values for δ and P indicating compression. Further, the modulus E is the same in tension and compression to a good approximation, and the stress-straincurve simply extends as a straight line into the third quadrant as shown in Fig. 15.
The first acquaintance of an engineering student with lab-controlled material behavior is usually through tension tests carried out during the first Mechanics, Statics and Structures sophomore course. Test results are usually displayed as axial nominal strain versus axial nominal strain, as illustrated in Figure 5.1 for a mild steel specimen taken up to failure. Several response regions are indicated there: linearly elastic, yield, strain hardening, localization and failure. These are discussed in the aforementioned course, and studied further in courses on Aerospace Materials. It is sufficient to note here that we shall be mostly concerned with the linearly elastic region that occurs before yield. In that region the one-dimensional (1D) Hooke’s law is assumed to hold. Material behavior may depart significantly from that shown in Figure 5.1. Three distinct flavors: brittle, moderately ductile and nonlinear-from-start, are shown schematically in Figure 5.2 . Brittle materials such as glass, rock, ceramics, concrete-under-tension, etc., exhibit primarily linear be- havior up to near failure by fracture. Metallic alloys used in aerospace, such as Aluminum and Titanium alloys, display moderately ductile behavior, without a well defined yield point and yield region: the stress-straincurve gradually turns down finally dropping to failure. Some materials, such as rubbers and polymers, exhibit strong nonlinear behavior from the start. Although such materials may be elastic there is no easily identifiable linearly elastic region.
The Dutch strain was originally collected from a polder near Utrecht, the Netherlands, in the 1950s, and has been laboratory- reared since then. This strain was brought to the University of Calgary in the late 1980s. Most of the work on L. stagnalis has been carried out on individuals reared from the Dutch strain. However, L. stagnalis present a unique opportunity in studies of learning and memory because strains of the same species from different geographic locations vary in cognitive ability. The majority of wild strains of L. stagnalis we have sampled exhibit learning and memory-forming capabilities identical to those of the Dutch strain. However, some populations of snails, freshly collected from certain ponds, are able to form a memory with only a single 0.5 h training session that persists for at least 24 h (i.e. ‘ smart ’ snails; Dalesman et al., 2011a,b,c). There is a growing body of evidence suggesting that populations of L. stagnalis differ in their LTM-forming capabilities as well as their responses to environmental stimuli (Dalesman and Lukowiak, 2012). Cognitive ability, as well as responses to environmental stress, are conserved in the wild as well as in successive generations reared in the laboratory, indicating a genetic or epigenetic basis to these abilities and responses (Orr et al., 2009a,b; Dalesman et al., 2011c). Our current, yet previously unsubstantiated, working hypothesis is that ‘ smart ’ snails are more easily stressed than ‘ average ’ snails (Lukowiak et al., 2014a). According to the Yerkes – Dodson/Hebb (YDH) law (Ito et al., 2015b), a good level of stress is a level the individual can cope with, but is sufficient to keep the individual ’ s
acteristic. It demonstrates the presence of some typical size which would make the fracture beginning inde- pendent of the cut end geometry. In our situation, the physical cut thickness is associated with this typical size, so there’s no point in discussing a form of its end. The introduction of average characteristics over the layer thickness makes it possible to dismiss the questions re- lated both to infinite stresses on the physical cut exten- sion in the continuous medium and to a form of the physical cut end, so the corresponding boundaries are shown in Figure 1 with a wavy line. The boundary stresses associated with average equilibrium conditions  are also considered for the layer. The layer/medium conjunctions are established by the layer boundary stresses on the surface which has no singular points and, as a consequence, has no singularity. The article  in- cludes solutions for infinite linear-elastic medium with the physical cut. The paper  for perfectly elastoplastic behavior of the layer material solves the analogue of the Dugdale problem  . This article provides general statement of the problem of damaged finite body strain- ing.
The design recommendation proposed by RILEM appears to overestimate the load-carrying capacity of prisms tested by the Brite-EuRam Project BRPR-CT98-0813 . To investigate the reliability of the RILEM stress-strain model, it is necessary to calculate the load mid-span deflection. For the finite element analysis undertaken by Dupont and Vandewalle of the Brite-EuRam project BRPR-CT98-0813  a relatively simple approximation of the stress-crack width curve was used as input for tensile stiffening. The final stress-strain relationship was then calculated by simply dividing the crack width by the characteristic length, which was assumed to be the length of one finite element. Dupont and Vandewalle  assumed the characteristic length to be 0.79h sp (h sp , prism effective depth) and the
material fails. We present a series of experiments on high purity, well characterized tantalum samples subjected to shock-loading via gas-gun plate impact. Through careful selection of the flyer-plate velocity and material we have independent control over the peak compressive stress and the tensile strain rate in the sample. At all times, the spall damage remains incipient, i.e. in the early stages of void formation and the material does not fully fracture. Velocimetry was used on the rear of the sample to record the wave-profiles and determine spall strength. Soft recovery and sectioning of the samples allowed the internal damage to be observed, quantifying the damage amount, distribution, and relationship to microstructural features with both optical and electron based microscopy.
It has been shown in  that the Masing and Memory models are not valid if the tempera- ture varies during the cycle. Masing based his finding on the rheological spring-slider model and assumed that the model parameters are time inde- pendent . Therefore, the spring-slider model has been adapted for variable temperatures ( and ). The model developed so far is capable of modelling elasto-plastic hardening solids and non-linear kinematic hardening under stress con- trol. If the strain is controlled, the rheological spring-slider model depicted in Fig. 1 proves to be more convenient.