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.
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
Although the typical cyclic stress-straincurve could be described by an analogy with Hollomon equation or Ludwik equation based on exponential ﬁtting, the ﬁtting precision might not be high enough with unsatisfactory correlation coefﬁcient if the stable hysteresis loops is insufﬁcient. As basic methods of static and dynamic mechanical tests, the tensile and low cycle fatigue tests have been widely adopted to determine the basic mechanical properties of structural materials. 7 12) Take the extruded AZ31B magne- sium alloy 8 12) with typical cyclic hardening behavior for example, S. Hasegawa et al. 10) investigated the low cycle fatigue behavior under uniaxial cyclic loading by both strain and stress controlled conditions, and a fatigue life evaluation method was discussed based on Manson-Cofﬁn equation, and Y. C. Lin et al. 11) studied the hot tensile deformation and
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.
DOI: 10.4236/jmmce.2018.63029 411 J. Minerals and Materials Characterization and Engineering experiments would vary on the unloading position and times. Several kinds of vehicle light-weight materials were adopted for the experiments, including AL6061, HSLA, Q195 and medium manganese steel. At the first step, a series of experiments were carried on AL6061, HSLA and Q195 to confirm the influence of unloading position and times, and the experiments were designed as Table 1. Firstly, the materials of the reference group were once pulled off directly for get- ting its total elongation according to the stress-straincurve. For each material, the total elongation of monotonic loading (TEML) was taken into account as the standard for the experiment affected by unloading positions or unloading times, and the percentage of the TEML was defined as the unloading position in all ex- periments. Secondarily, the unloading-reloading tensile experiment would un- load at 50% of the TEML for once while the twice and three times unloading ex- periments would unload at 33.3% - 66.7% and 25% - 50% - 75% of the TEML in turn with a constant rate, respectively. Furthermore, the deformation would be contrasted by strain-stress curves in the same coordinate system. At the second step, corresponding comparative experiments were designed to come up with the constitutive correction function decided by unloading position and times through data analysis and curve fitting. The material of medium manganese steel was applied and the comparative experiments were designed as Table 2. The monotonic loading test in the comparative experiments is designed as the refer- ence group of the once unloading tests, which include three different groups unloading at 25%, 50%, 75% of the TEML. Additionally, there are two groups of twice unloading tests and one group of three times unloading test. The twice Table 1. Comparative experiments of AL6061, HSLA, Q195.
Most of the alloys like titanium, steel, brass, copper, etc., are used in engineering applications like automobile, aero- space, marine etc., consist of two or more phases. If a material consists of two or more phases or components it is very difficult to predict the properties like mechanical and other properties based on simple laws such as rule of mixtures. Titanium alloys are capable of producing different microstructures when it subjected to heat treatments, so much of money and time are squandering to study the effect of microstructure on mechanical properties of titanium alloys. This squandering can be reduced with the help of modeling and optimization techniques. There are many modeling tech- niques like Finite element method, Mat lab, Mathematical modeling etc. are available. But Finite element method is widely used for prediction because of capable of producing distributions of stresses and strains at any different loads. From the literature it is observed that there is a good agreement between the calculated and measured stress strain curves. This review paper describes the effect of volume fraction and grain size of alpha phase on the stress straincurve of the titanium alloys. It also can predict the effect of strength ratio on stress straincurve by using FEM. This informa- tion will be of great use in designing and selecting the titanium alloys for various engineering applications.
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.
With sufficient soil testing, all of the soil parameters can be addressed. Given the material properties discussed for linear analysis, only the post yielding shear stress versus shear strain parameters can be calibrated. Also, to use the available material properties as linear analyses use them, the post yielding shear stress versus shear straincurve must be held constant rather than allowing them to vary with mean effective stress (where varying with mean effective stress is more realistic).
ABI technique is, in fact, a kind of progressive multiple loading and partial-unloading continuous indentation experiment in the same point. A spherical indenter is pressed into the polished sample surface at a constant speed in the normal direction, and load and displacement are measured simultaneously in real-time using load and displacement sensors. Then a continuous curve of the indentation test process (load-indentation depth curve) is obtained. Finally the load-indentation depth curve can be changed into the true stress and true plastic straincurve of material to gain various material properties, including the yield strength, tensile strength, strain hardening exponent and strain-hardening coefficient, and so on (Kim and Baik et al, 2012; Jia and Xuan, 2012; Lee and Kim et al, 2008).
appreciably. This softening e ﬀ ect can mask and moderate strain hardening, which are observed under quasi-static loading conditions, and can even cause a decrease in the stress-straincurve of the solid. Thus, the dynamic loading by the Kolsky bar system cannot be simply interpreted as a high strain rate test, since it contains, inherently, the thermal softening mechanism. This coupling, between high strain rate and thermal softening, can be prevented by loading the specimen repeatedly, in such a way that the specimen deforms only slightly during each loading. In this study we performed a series of tests with multiply loaded specimens, made of diﬀerent aluminum alloys, and compared their stress-strain response to that achieved by a single high strain loading. As expected, we found that due to lack of thermal softening, the stress-straincurve from the multi-step test is higher than that from the one-shot test.
stresses is shown in Figs. 6 and 7. A comparison between Figs. 6(a)–(b) and 7(a)–(b) shows how the stress versus straincurve is markedly altered by small superimposed tensile mean stress for a constant temperature and given strain rate, while no significant effect of compressive mean stress on free vol- ume concentration is observed for the same range of mean stresses, which may explain the emergence of multiple shear bands prior to failure under localized indentation.
The risk of hot cracking was estimated in the same way as in Nasser (2012) and Chen and Hao (2010). In each location the computed equivalent plastic strain was plotted against temperature. This was performed only for one weld pass in the location of interest. The critical strain for ductility dip cracking (Figure 8) is plotted together with the computed results in Figure 12 and Figure 13. This critical straincurve was utilised for the both mock-ups due to lack of material specific data.
The TDFADs for selected cases in Table 2 are shown in Fig. 4(a) to (c). Similar to the equivalent isochronous stress-straincurve (EISSC) being a weight average of isochronous stress-strain curves of base and weld materials, the modified TDFADs constructed from the EISSC and the equivalent 0.2% proof stress lie between the TDFADs of the weld and base materials. For over-matching weldment (M>1), the failure assessment curves always lie over that of evenmatched welded cylinder made of base metal, and for under-matching cases (M<1), the failure curves are always located below that of evenmatched welded cylinder made of base metal. Fig .4 also indicates the influences of combined parameter ψ on the modified TDFAD. When the value of ψ decreases, the TDAFD of mismatched welded cylinder closes to that of homogeneous cylinder made of weld metal. While with the value of ψ increasing, the TDFAD gradually closes to that of homogeneous cylinder made of base metal.
Details of the plastic strain region of the stress-strain curves obtained in the tensile tests at room temperature, 200, 300 e 500 °C are shown in Figure 5. Note that even at room temperature, a slight oscillation in stress occurs. However, with a much smaller amplitude when compared to the serrated observed on the test at 500 ° C. The stress-straincurve at 200 °C showed an A-type serrated, while at the 500 °C it was observed B-type serrated. This B-type serrated occurred in the test temperature range between 400 and 700 °C. In the tensile tests at 300 °C, a transition appears to occur, with serrated A+B-type. The predominance of A and B-type serrated in the tensile test curves at low temperatures and high strain rates are consistent with previous work [7,12,17–19]. A and B-type serrated are related to the diffusion of C atoms in Ni-based alloys . The C-type serrated was not observed in the stress-strain curves, it should only appear in tests at high temperatures and low strain rates that were not used in this work.
stress-straincurve is represented by a bilinear curve. The first slope represents the elastic modulus up to the yield stress, and the second slope represents a linear plastic modulus. When a material is loaded into the plastic range and subsequently unloaded, the reverse path follows the elastic slope back to a range of twice the yield stress and then follows the plastic slope. The ANSYS program also provides a multilinear kinematic hardening (MKIN) option based on the Besseling multilayer model . When this rule is applied, the stress-straincurve is represented by several linear segments. This allows for a more accurate representation of a stress-straincurve. Under reversed loading, the load path again follows the elastic slope back to twice the yield stress and then follows the path of the multiple plastic slopes. However, using either rule, the plastic modulus is always the same for loading and unloading and is unaffected by the presence of a mean stress. As a result, for a prescribed uniaxial stress cycle with a mean stress, the loading and reversed loading hyteresis curves will always produce a closed loop with no ratcheting.
structures operating under fatigue and creep conditions, as illustrated in Fig. 1. It is conventionally defined in context of a cyclic stress-straincurve (SSC), which is obtained from results of cyclic tests for a number of different strain ranges. Each cyclic test produces a stabilised stress response, which is effected either by hardening or by softening depending on the type of steel. In the case of steels with a cyclic softening effect, σ c y separates the low stress range of purely elastic behaviour from moderate stress range of mixed elasto-plastic behaviour. Monotonic yield strength σ m
At both testing temperatures, off-axis specimens com- pressed the second time (Fig. 4) have a stress-straincurve that resembles the stress-straincurve of specimens loaded in the transverse direction (Figs. 1, 2): After an initial in- crement of compressive stress as a function of increased compressive strain, a plateau region appears where stress changes only slightly along with strain, the change of stress again accelerating at compressive strains exceeding 40%. It is worth noting that at 131°C the stress response to any given strain is greater in once-compressed off-axis speci- mens (Fig. 4b) than in once-compressed longitudinal speci- mens (Fig. 3b).