Stress and Strain Physics - Coursework Example

? Stress and Strain Introduction The dynamics of rigid bodies consist of objects with definite shapes and sizes, although the particles that make up these objects are inhibited such that the relative positions of those particles do not change. That is, these rigid bodies do not ever squeeze, stretch or twist. However, we are certain that this do occur in reality. This makes up our research problem because we need to find an explanation for this concept. We shall do this by looking into the concepts of strain and stress. Strain is a measure of any particular change in the shape of an object while stress is a measure of the strength of a particular material. Because of this research problem, we will incorporate the concept of elastic modulus to help understand the problem and address the research question. Elastic modulus is a measure of the amount of the stress required to make a change in the shape of an object (Redman, 2006). The question of research The major research questions that this research seeks to investigate and address are the concepts and the basic terms of stress and strain. The research will also look into various types stress and the mathematical formulae and equations involved in understanding the concepts investigated. Finally this research paper will look into the stress strain curve. This research paper will help us understand the variability and relationship between stress and strain, this will enhance our ability to standardize the equations and the variables involved in the concepts of strain and stress. The main objective of this research papers is to shed light on the concepts of strain and stress and to address the relationship between the two terms. The equations and formulae involved are just to help us conceptualize and master the two concepts in addressing our research problem stated in the introduction above. Abstract This research paper will be carried via a series of investigations on the definition of the basic terms and concepts involved. Stress as been defined as force per area, a ration of force applied on a cross sectional area. This measures the strength of a material determined by the quantity of pressure a material can stand without getting into some sort of deformation or physical change. On the other hand, strain is a deformation due to a twist of a solid due to the action of stress. This gives the extent to which an object is stretched due to stress. Hence strain in a product of stress or rather stress causes strain. As stated earlier in the introductory part of this research paper, we will look into various types of stress which will be elaborated in the subject of research area. Generally there are three distinct types of stress that results from subjecting an object to stress. If an object is compressed or stretched, that particular object is subjected to what we refer to as a tensile stress. If another object if put under a force a long a whole surface and the volume of the object is altered, then we refer to that particular experience as a bulk stress. Lastly, it acts tangentially to the surface and results into a twist of the object, then we refer to that as a shear stress (Tipler, 1995). As the major objective of this research paper, we are going to investigate some of the major concepts of stress and strain that will help us as students to understand the two terms. Some of the major concepts that we as students may find challenging when learning about stress and strain include: Deformation of rocks; we often difficult for us to realize that rocks too get broken or bent. It is also challenging to realize the forces responsible for events such as faults and folds. This can be seconded by those who live in areas which are tectonically stable and have never experienced any such thing as tremors. If we have to understand the basic terms of strain and stress, we must therefore rise above this barrier because it will not be easy to understand the conditions and causes of deformation if we cannot comprehend the word deformation itself. Therefore in order to understand rock deformation as a concept of stress and strain, we can use some pictures and samples of real folded and faulted rocks. With those practical examples, we will be able to understand what really causes deformation of those rocks. Another concept that we will look into is that stress causes strain and that strain results in structures; it is vital to us as students to understand that the visible structures are merely records of stress and the physical earth conditions. It is an act of stress on the structures that eventually leads to strain on the objects. Strain may result into formation of a completely different structure from the original structure in which stress was exerted. For us to understand this, we can literally hit an object with another heavier solid against a surface and witness the result. The other concept that we will be interested in investigating is that different conditions result into different styles of deformation; it is true that distinct factors contribute to different deformation styles (Halsall, 2008). These factors may include temperature, pressure, and the type of stress, composition of the rock, rate of stress, absence or presence of some fluids among others. Hence, we can see the different styles of deformation by practically subjecting a rock to stress under varied conditions mentioned there before to witness the style of deformation in each particular combination of conditions. We will also look into the concept of inferring and relating faults to stress; we can understand this by relating the nature of the deformation with the stress that brought it about. Here, it will be of significance to us to differentiate between the reverse fault resulting from compression and normal faults caused by tension. In order to understand this, we will use wooden blocks to learn about the reverse and normal faults. We can cut the blocks on an angle and generate grabens and horsts (Young, 2001). We will then pull apart the blocks to generate a graben and make a horst by pushing them together. This will enable us to understand the distinction between the reverse and the normal faults. We will be able to realize that the hanging block moves up to create a reverse fault due to compression and at the same time if he hanging wall moves down, a normal fault is created due to extension. Finally, we will look into the concept of relationship between the reality and analogs; this is because it is the analogs which are normally used to illustrate the other concepts of strain, stress and the actual deformation of the rocks. This will help us eliminate the difficulty in relating the analogs to the real rocks and the behavior of the earth (Tipler, 1995). We will therefore achieve this by discussing the magnitudes and rates of the deformation of the earth and the distinction between rocks and analogs. For example, one may realize that the rocks at the plate boundaries usually experience very minimal deformation in a year although the forces exerted on them are often enough to shake continents. The subject of research The subject area of research is physical geology and physics which entails the space and earth science. In this particular subject area of research stress is studied and defined as the force exerted in a specified area, i.e. force per unit area. Nevertheless, stress in particularly complex in quantity compared to pressure due to the fact that it varies with both the surface and the direction in which it acts. Some of the basic terms that are involved include: compression, which is a stress that shortens an object; tension, which is a stress that results into lengthening an object; normal stress, is that which occurs perpendicularly on a surface, this can either be tensional or compression; shear, which acts in parallel to the surface, it may cause the object to slide over the other or deform rectangular objects to parallelograms; hydrostatic, is that stress which acts uniformly in all directions; and directed stress, which varies depending on the direction (Halsall, 2008). Generally, we never get the chance to see stress; we only witness its results after deforming the objects. On the other hand, the subject area of research defines the major terms used in strain, the quantity of deformation experienced by an object compared to its initial shape and size. For instance, a block measuring 20cm on a side may get deformed and becomes 18cm long. In that particular case, the strain is (20 – 18) / 20 (Baker, 2007). This may be expressed as a percentage. It is however important to realize that strain has no dimension. The basic terms involved in strain therefore include: linear or longitudinal strain, which is that strain which distorts the length without altering the direction (Karl, 2010). This can be tensional or compression; compression, a longitudinal strain which makes an object shorter than its original length; tension, a longitudinal strain that makes an object longer that it was originally; shear, which is a strain that alters the angle of the object. It might cause rotation of lines; infinitesimal strain, a tiny strain which is of less percentage. This usually allows significant approximations and simplifications of mathematics; finite strain, a larger strain of bigger percentage which needs much complicated treatment mathematically than infinitesimal; homogeneous strain, which is a uniform strain where the straight lines in the initial object remains just as straight as they were, parallel ones remain parallel as well; and inhomogeneous strain, where there is a variation in deformation from place to place. This might result into lines bending but not remaining necessarily parallel (Young, 2001). Consequently, the objects and materials that experience stress and strain also behave in a particular way. Some of the terms associated with the nature of these materials include; elastic, where a material get deformed when under stress but regains its original shape and size when released from stress; brittle, these are materials that get fractured upon deformation; ductile, materials that get deformed but remain unbroken; viscous, materials that steadily deform when under stress; plastic, materials which only get deformed when the threshold of the stress is exceeded; and viscous-elastic materials which combines both the properties of the viscous and elastic materials (Baker, 2007). Conclusion It is in order therefore to give an illustration of the stress strain curves for various materials such as ductile materials and brittle materials in order to master the difference between the two. The following shows a graph indicating the relationship between stress and strain Source: (Tipler, 1995). Stress can be shown in a graph against strain. The stiffness of an object, the extent to which the object can stand stress is similar to the area under the curve that is between the fracture point and the y axis. This graph therefore shows how stress can impact on a material. The stress strain graph above represents a low carbon steel material. At the elastic region, between point 2 and the origin, the ratio between strain and stress is constant; hence the material remains obedient to the Hooke’s law which asserts that the material is elastic if a force and extension are directly proportional to each other. At the plastic region, between point 2 and 3, the rate of increasing extension is rising up and the material has already passed the elastic limit. At this point, the material can no longer return to its initial shape. Just after the first point, 1, the quantity of stress reduces because of the necking and hence the material in question will extend much under a lesser force. The final point is the fracture point, point 3, where the material eventually fractures or breaks and the curve comes to an end (Young, 2001). The following is a graph showing the relationship between stress and strain in a brittle material Source (Tipler, 1995). Brittle substance such as carbon fiber and concrete does not have a point of yield and therefore does not strain harden. The breaking strength and the ultimate strength are hence similar. The graph above hence indicate that typical brittle objects does not demonstrate any kind of plastic deformation but just fails as the deformation if elastic. One of the features of brittle material failure is that the broken parts may produce the same shape like the original if they are reassembled because neck formation will not be there like in ductile materials. An archetypal stress strain curve for the brittle materials is linear (Tipler, 1995). To sum up, stress and strain are two related concepts that can be confused if not mastered keenly. Strain is a result of stress. The definitions of the two should be clearly stated to avoid misconceptions. This research paper has therefore generally given the concepts and the basic terms involved in stress and strain. The two have been clearly distinguished and described. We can therefore boldly assert that the research problem has been addressed. Bibliography Baker, R., 2007. Stress and strain concepts, Boston: Springer Halsall, P., 2008.  Basic terminologies of Stress and Strain, London: Fordham University.  Karl, P., 2010. Physical Geology, Boston: McGraw-Hill Redman, P., 2006. The relationship of Stress, strain and rock deformation, Cambridge: Cambridge University Tipler, A., 1995. Physics for Scientists and Engineers, London: Worth Publishers. Young, W., 2001. Roark's Formulas for Stress and Strain, New York: McGraw-Hill.   Read More