relation shows that the smaller the grain size, the larger the flow stress. The Hollomon's equation which is a power law relating the true strain. Two explanations of this power law relationship have been proposed. One, due to Fisher and Holloman, is that a certain number k (equal in this case to six or. The power law flow equation, such as Holloman stress–strain relation, having an unbounded prediction of maximum stress attainable by strain.
K and n are fitting constants usually termed as strain These relationships are purely empirical in nature hardening coefficient and the strain hardening expo- and are not based on physical arguments involv- nent respectively.
K and n are easily determined from a ing dislocation theory. The relative efficacies of var- double logarithmic plot of the experimental true stress- ious constitutive equations have been compared earlier true strain data. Many deviations from the Holloman [10—12]. Efforts are made time and again to understand relation have been reported.
The anomalous variation of flow parame- sectional area. For instance, work hardening rate has an influence on 3. Results and discussion formability, ductility and toughness. The exponent n The true stress-true plastic strain curve segments from plays a crucial role in sheet metal forming.
The larger single specimen data and multiple specimen data are the n value, the more the material can elongate before shown in Fig. It is observed that they almost match necking and the material can be stretched farther before within the normal specimen-to-specimen variation. In cup drawing high n values may reduce Fig.
The single specimen easily when the blank holder force is increased. A good data also followed the same trend. It is observed that machineable material should have low fracture tough- the type steel at room temperature does not obey a ness and low strain hardening index n, while the reverse power relation suggested by Hollomon.
It is well known that the Ludwigson  suggested that the observed devia- tendency to elastic spring-back increases with increase tion from the Holloman relation in stainless steels and in strength coefficient and with decrease in the elas- other low stacking fault energy materials is due to the tic stiffness.
The value of spring-back angle decreases change over of planar slip at low strains to cross slip with increasing value of strain hardening exponent. In the present study we examine the stress strain be- He had introduced a correction term that depends on haviour of prior cold worked Type austenitic stain- plastic strain, to account for the stress deviation from less steel and the deviation from Hollomon relation.
Hollomon relation at low strains as the second term in In particular we examine the Ludwigson equation and Equation 2. The various parameters derived deviation from Holloman equation is a consequence of from the plots in Fig. Experimental Type stainless steel having chemical composition wt. No laboratory re-solution annealing was given Figure 1 True stress—true plastic strain curve segments for the type to the material.
Tensile specimens with 25 mm gauge stainless steel with different prior cold work levels. Spec- imens in the mill-annealed condition was tested at room temperature in uniaxial tension at a nominal strain rate of 3. Another set of specimens was prior deformed to 7. True stress, true plastic strain and work hardening rate data were computed for mill-annealed and prior deformed tests Figure 2 Double logarithmic plot of true stress-true strain data as a after correcting for the change in gauge length and cross function of prior cold work.
Truncating the data at small strain ranges affect the fitting parameters.True stress, true strain and work hardening
The fitting parameters in Table I are obtained as the best fit parameters and their varia- tion with r is also shown in Table I. It is interesting to note that the strength coefficient K and strain-hardening index n vary with the amount of PCW or pre strain.
In Stage III which was the material was given a prior cold work of In all the three TEM studies, the occurrence then either from the material tested after giving a prior of cross slip was seen at strains 1. It is observed that ing from 0.
The data are plotted in a double in either case this does not happen and the transient logarithmic graph as shown in line a Fig. At normal temperatures the dislocations are not annihilated by annealing. Instead, the dislocations accumulate, interact with one another, and serve as pinning points or obstacles that significantly impede their motion.
This leads to an increase in the yield strength of the material and a subsequent decrease in ductility. Such deformation increases the concentration of dislocations which may subsequently form low-angle grain boundaries surrounding sub-grains. Cold working generally results in a higher yield strength as a result of the increased number of dislocations and the Hall—Petch effect of the sub-grains, and a decrease in ductility.
The effects of cold working may be reversed by annealing the material at high temperatures where recovery and recrystallization reduce the dislocation density.
A material's work hardenability can be predicted by analyzing a stress—strain curveor studied in context by performing hardness tests before and after a process. Deformation engineering Work hardening is a consequence of plastic deformation, a permanent change in shape.
This is distinct from elastic deformation, which is reversible. Most materials do not exhibit only one or the other, but rather a combination of the two.
Notes on Stress-Strain Relationship
The following discussion mostly applies to metals, especially steels, which are well studied. Work hardening occurs most notably for ductile materials such as metals.
Ductility is the ability of a material to undergo plastic deformations before fracture for example, bending a steel rod until it finally breaks. The tensile test is widely used to study deformation mechanisms. This is because under compression, most materials will experience trivial lattice mismatch and non-trivial buckling events before plastic deformation or fracture occur.
Hence the intermediate processes that occur to the material under uniaxial compression before the incidence of plastic deformation make the compressive test fraught with difficulties. A material generally deforms elastically under the influence of small forces ; the material returns quickly to its original shape when the deforming force is removed.
This phenomenon is called elastic deformation. This behavior in materials is described by Hooke's Law. Materials behave elastically until the deforming force increases beyond the elastic limitwhich is also known as the yield stress. At that point, the material is permanently deformed and fails to return to its original shape when the force is removed.
This phenomenon is called plastic deformation. For example, if one stretches a coil spring up to a certain point, it will return to its original shape, but once it is stretched beyond the elastic limit, it will remain deformed and won't return to its original state. Elastic deformation stretches the bonds between atoms away from their equilibrium radius of separation, without applying enough energy to break the inter-atomic bonds.
Plastic deformation, on the other hand, breaks inter-atomic bonds, and therefore involves the rearrangement of atoms in a solid material. Dislocations and lattice strain fields[ edit ] Main article: Dislocation In materials science parlance, dislocations are defined as line defects in a material's crystal structure.
The bonds surrounding the dislocation are already elastically strained by the defect compared to the bonds between the constituents of the regular crystal lattice. Therefore, these bonds break at relatively lower stresses, leading to plastic deformation. The strained bonds around a dislocation are characterized by lattice strain fields.
For example, there are compressively strained bonds directly next to an edge dislocation and tensilely strained bonds beyond the end of an edge dislocation. These form compressive strain fields and tensile strain fields, respectively.