I have a very important for statics class - Lab Report Example

A fracture may be experienced if a strain continues beyond the proportionate limit. At zero the graph is starting to form linearity, however it reaches at 100 when it starts to decrease which can be associated with the proportionate limit. b) The graph of stress against strain reduced in a range just larger than the original portion. 2. a) Straine) is the fractional length change of a stretched material, while stress (?e) is the force per unit area of the stretched material. Therefore, deformation is a change in the size or shape of the object.

Strain=  Stress =  and has SI units which are the same as those of pressure N/m2 or Pa . Where A is the initial cross-sectional area, Lo is the initial gauge length , and L is the change in gauge length. According to Hooke’s law, the deformation is proportional to the deforming forces as long as they are not too large. F= k L where k is constant and it depends on the length and cross sectional area of the object. So Hooke’s law written in stress will be  = And length change is ( L) is proportional to the magnitude of the deforming forces, Y depends on the inherent stiffness of the material from which the object is composed.

k = Y , therefore, Y is the constant of proportionality called Young’s modulus which will be given by the slope of the stress-strain curve. Young’s modulus or elastic modulus has the same units as those of stress (Pa or N/M2) and can be thought of as the inherent stiffness of a material because it measures the resistance of the material to elongation or compression. So, materials that stretch easily and are flexible such as rubber have low Young’s modulus. While materials that are stiff such as steel have high Young’s modulus; it takes a lager stress to produce the same strain.

From data young’s modulus is calculated as change in y-axis divided by change in x-axis Y (slope) = = = 2.117610 Young’s modulus (E) from the data is 2.117610Pa b) Yield stress is the stress which is required to deform the material it is at that point when a permanent deformation takes place. It is usually at 0.2%; in this case of aluminum yield stress begins at 0.4%. At the point there is intersection between strain and yield stress and strain is called off-set stress. As strain is increased, many materials eventually deviate from this linear proportionality, the point of departure being termed the proportional limit.

This nonlinearity is usually associated with stress-induced “plastic” ?ow in the specimen. Here the material is undergoing a rearrangement of its internal molecular or microscopic structure, in which atoms are being moved to new equilibrium positions. This plasticity requires a mechanism for molecular mobility, which in crystalline materials can arise from dislocation motion. Materials lacking this mobility, for instance by having internal microstructures that block dislocation motion, are usually brittle rather than ductile.

The stress-strain curve for brittle materials are typically linear over their full range of strain, eventually terminating in fracture without appreciable plastic flow. c) Ultimate stress/ strength is the maximum stress that can be withstood without breaking. It is the stress which is called true stress it is calculated as  = ?u - ?0.2 The stress at the ultimate strain is calculated as shown below ?t= ?u (l+e) where ?t= 0.2, e=11918.55 ?t= ?u