Introduction
How materials behave is dependent on various factors, some of which include their mechanical properties. When the material experiences various loading conditions, its behavior reflects its mechanical conditions as well as the effect of the loading conditions. When a material experiences various loading conditions, the material experiences either shear stress, tensile strength, or compressive strength. The tensile properties of a material relate to its ability support any axial loads to which it is subjected without rapturing (Department of Engineering. 2007).
When a material is subjected to tensile stress, the deformation that occurs is in the form of elongation or stretching. This means that its circumference reduces as more axial loads are added. In compressive stress, the material is subjected to axial compression, the result of which is the material becomes shorter in length. Depending on the amount of axial compression and whether there is lateral resistance, the circumference of the material might increase. Shear stresses act on a direction that is tangential to the point at which the axial loads are exerted. When stress is exerted on a material, strain occurs (Department of Engineering. 2007).
Strain refers to how a material changes in reaction to the stress to which it is subjected. Strain measures the proportion of change to the shape of a material as a result of the stress to which it is subjected (Department of Engineering. 2007). The stress-strain relationship is very important in engineering because it influences the choice of material among other factors. This relationship is affected by various factors. This report explores how these factors affect the stress and strain relationship in a material. The understanding of these factors is important from an engineering perspective because it not only influences the choice of materials, but also the manner in which the material is used and the amounts of axial loads to which different materials can be subjected at different conditions without deforming the material.
Theory
The relationship between strain and stress in the mechanics of solids can be explained using the Hooke’s Law. Hooke’s Law holds that the stress to which an object is subjected is directly relational to the resultant strain when the material is question is loaded without exceeding its elastic limit (Department of Engineering. 2007). This Law can be explained through the diagram below:
Figure 1 showing the stress-strain diagram
(Source: Department of Engineering. 2007).
Hooke’s law described a linear relationship between stress and strain. In this relationship, the upper stress limit is known as the proportional limit and it is denoted by A in Figure 1 above (Department of Engineering. 2007). The elastic limit of the material in question is denoted by B in Figure 1. Any stress to which a material is subjected between A and B does not enjoy the linear relationship described by Hooke, meaning that it is not directly relational to the resultant strain (Department of Engineering. 2007). However, the stress between the two points does not cause strain on the material, hence, it retains its initial size upon the removal of the load. The elastic limits and the proportional limits of many materials are close. The point denoted C in Figure 1 above is known as the yield strength (Department of Engineering. 2007).
If a material is subjected to loads that exceed the yield stress, plastic deformation takes place. This means that the even after the removal of the axial loads, the initial size of the material will not be retained and the deformation of the material is permanent (Department of Engineering. 2007). If more load is subjected to a material which has already experienced the permanent deformation as a result of loads exceed the yield stress, the amount of strain is significantly more for an increase in stress my small amount. If the loads exceed the ultimate stress which is denoted as D in Figure 1 above, there is a rapid decrease in the cross-sectional area of the material. The continued loading of the material will cause a fracture which is denoted as E in Figure 1 above (Department of Engineering. 2007).
Methods
The methodology to be used is the review of secondary sources. A lot of scholarly work has been done on the factors that influence the stress and strain properties of materials. A review of literature in this field of study will help identify the factors that influence the stress and strain of materials as well as the mechanisms through which the effect is achieved. The sources that will be reviewed will be scholarly or peer reviewed in nature. This is an important inclusion criterion because the credibility of the authors and the sources is important to the veracity of the information presented therein. Additionally, the various empirical models that are used to explain the effect of various factors are derived through mathematical computations. It is important that the credibility and mandate of the authors are verified first as a credible source.
Results
In their work on the conrellaiton between the true stress-strain curve and the engineering stress strain curve, Faridmehr et al., (2014) identified the direction of loading as a significant factor that affected the relationship between stress and strain. Homogeneity and fatigue were identified as significant factors by Zhu &Tang, (2004) and Frunza & Diaconescu, (2006) respectively.
Discussion
One of the factors highlighted as being influential to the stress and strain of a material was homogeneity. Homogeneity refers to the aspect of an object containing the materials through its entire structure. For instance, a beam used in the construction of trusses will be regarded as homogenous if its entire structure is made of one materials. This means that the entire beam is made of cast iron or steel. Homogenous materials cannot be separated into various units through mechanical means.
Some examples of homogenous materials include resins, glass, board, metal, ceramics and alloys. The homogeneity of materials is also understood through other concepts such as isotropy, anisotropy, and orthotropy. Isotropic materials are characterized by a similarity in the values of a given property of the material in all the planes of the material. For instance, the Young’s Modulus of such a material would be uniform in all the directions of a material. This characteristic has an influence on the stress and strain because the application of constant axial loads on different points of the material has the same effect.
There are also anisotropic materials. Anisotropic materials are different from isotropic materials in that the values of various physical properties are dependent on the direction of the object. The implication is that the value of a physical property such as the Young’s Modulus is different with the direction. Some of the materials that have this characteristic include composites of different materials and wood. Orthotropic materials are a type of anisotropic materials because their physical properties vary when they are measured from different directions.
This is to mean that the value of a given physical property when measured from the transverse direction is different when the same value is measured from the lateral direction. The implication is that the stress acting on the object when similar axial loads are placed on different directions along the object is different. By extension, the strain on the material when similar axial loads are placed along the object in different directions is different.
The direction of loading is another factor that influences the stress and strain properties of materials. There are different directions of loading to be considered. Some of them include compression, tension, shear, bending, and combined loading. With the tension direction, the material experiences forces that are equal and opposite. The forces are applied outwards emanating from the object’s structure. Compression direction of loading is different in that equal forces are applied towards the object’s surface as shown in Figure 1 below.
Figure 2 showing the tension and compression direction of loading
(Source: Department of Engineering. 2007).
The bending direction of loading combines both tension and compression forces. The tension and compression forces act against a neutral axis and the amount of stress to which the object is subjected using the bending load of direction is proportional between the point on the object where the forces are being applied and the neutral axis. This means that the larger the distance between the two points, the higher the stress to which the object is subjected. In application, there will be more deformation in the pipe where the distance between the neutral axis and the point where the tension and compression forces are acting on the pipe is longer compared to a pipe where the distance is shorter even if the two pipes are made of the same material with similar mechanical properties and are also subject to the same tension and compression forces.
The shear direction of loading cause stress and strain to a material when the material is subjected to forces that act in a parallel direction to the object’s structure. For instance, Figure 2 below shows a force F that is acting at both tips of the object. It is also evidence that the two forces are acting towards different directions, are equal, and are parallel to the direction of the objects structure. The resultant strain is caused by the shear direction of loading. If a neutral axis is introduced midway of the object, the sheer stress will result in a deformation that is characterized by rapturing on the neutral axis or a bending motion.
Figure 3 showing sheer stress
(Source: Department of Engineering. 2007).
Fatigue is another factor that influences the stress and strain properties of materials. Fatigue can occur in two forms. It can occur acutely where the integrity of the molecular structure of the material is undermined within a short term and chronically where the integrity of the molecular structure of the object is undermined over time due to repeated and cumulative events. The degeneration of the molecular structure of the object is the result of various factors. One of the factors that influences the degeneration of the molecular structure of an object is the magnitude of stress.
Objects which are exposed to high amounts of stress will degenerate and fatigue faster when compared to similar objects subjected to a smaller amount of stress. The total number of stress events is also a factor that influences the degeneration of the molecular structure of an object. Even if the amount of stress is small, an object that is exposed to more stress events will degenerate quickly when compared to a similar object that is subjected to a small number of stress events. The degeneration of the molecular structure is also affected by the frequency of the stress events.
The frequency in this instance relates more to the recovery time than the total number of stress events. When the frequency is high, there are more stress events within a unit period of time compared to when the frequency is low. A low recovery tome will predispose the object to more degeneration compared to a similar object that is allowed more recovery time between stress events. Fatigue is also influenced by the intrinsic integrity of the molecular structure. Even if the materials are isotropic in nature, their molecular structure might be compromised. Materials with fatigue are more likely to experience more strain from a smaller axial load compared to similar materials without fatigue.
Conclusion
The choice of materials in engineering is important because it affects the integrity of the object. The fact that the materials are used to support other materials in the implementation of design makes the behavior of materials under different axial loads and loading conditions of important to an engineer. Robert Hooke described a linear relationship existing between stress and strain. However, this relationship is dependent on various conditions as illustrated by the stress-strain curve. The discussion of factors that influence the stress and strain of materials shows that different directions of loading, differences in fatigue, and homogeneity affect the stress and strain behavior.
Recommendations
It is recommended that engineers consider the homogeneity of materials, direction of loading, and the factors affecting fatigue when choosing the materials for different engineering applications. It is also recommended to consider the axial loads to which the materials will be subjected inclusively with the other factors when deciding on the best materials for different engineering applications.
References
Faridmehr, I. , Osman, M. H. , Adnan, A. B. , Nejad, A. F. , Hodjati, R. , & Azimi, M. (2014). Correlation between Engineering Stress-Strain and True Stress-Strain Curve. American Journal of Civil Engineering and Architecture, 2(1), 53-59.
Frunza, G. and Diaconescu, E. (2006). Hysteresis and mechanical fatigue. The Annals of University “Dunarea de jos’ Galati Fascicle, 8(12): 61-66.
Zhu, W. and Tang, C. (2004). Micromechanical Model for Simulating the Fracture Process of Rock. Rock Mechanics and Rock Engineering. 37(1):25-56.
