The Behaviour of Ductile and Brittle Material on Different Loading Conditions (Recovered)

DEPARTMENT OF MECHANICAL ENGINEERING

Machine Design Home Assignment-I

SUBMITTED BY SUBMITTED TO: Bhaskar Raja Maharjan Nawaraj Baral 062BME610 Mechanical engineering

Mr. Department of

Date:2065/08/30

The behaviour of ductile and brittle material on different loading conditions Designing a product is a very crucial task because there may be all lot of money and life of many people depending on the success of the product. So, we have to consider many things while designing a product and proper selection of material is one of them. We have to know the nature of material before designing any product and we should know the behaviour of the material on different loading condition. If proper selection of material is not undertaken then there will be the failure of the product which may cause loss of money, time and in some cases human life as well. The materials are of majorly two types on the basis of their behaviour on loading conditions. They are: 1) Ductile material –A ductile material is the one which shows extensive plastic deformation before fracture. In a ductile material, the molecular bonds gradually break and re-form. The material can be greatly bent and reshaped without breaking (like soft metals or plasticene).Ductile materials can accommodate local stress concentrations, and they tend to hang together and survive after earthquakes and similar damage. The strength of ductile material is approximately the same both in tension and compression. Examples of ductile materials: Steel, Aluminum, Plastic, copper etc. 2) Brittle Material – A brittle material fractures without significant yielding. Brittle materials tend to be stronger in compression than tension. In a brittle material, all the molecular bonds break suddenly at a certain stress level. The material fails suddenly (like glass or brick). Brittle materials have only a small amount of elongation at fracture. When brittle materials fail, they do it suddenly and catastrophically. Brittle materials often have relatively large Young's moduli and ultimate stresses in comparison to ductile materials. Examples of brittle materials: Cast Iron, Ceramic, Phenolic etc.

The manner of computing the design stress depends on the manner of loading and on the type of material. Loading types include the following: 1. Static 2. Repeated and reversed 3. Fluctuating 4. Shock or impact 5. Random The primary factors to consider when specifying the type of loading to which a machine part is subjected are the manner of variation of the load and the resulting variation of stress with time. Stress variations are characterized by four key values: – Maximum stress, σmax – Minimum stress, σmin – Mean (average) stress, σm – Alternating stress, σa (stress amplitude) The maximum and minimum stresses are usually computed from known information by stress analysis or finite element methods, or they are measured using experimental stress analysis techniques. Then the mean and alternating stresses can be computed from: σm = (σmax + σmin) / 2 σa = (σmax- σmin) / 2 The behavior of a material under varying stresses is dependent on the manner of the variation. One method used to characterize the variation is called stress ratio.  Stress ratio R = minimum stress /maximum stress= σmin/ σmax  Stress ratio A = alternating stress /mean stress = σa /σm 1. Static stress When a part is subjected to a load that is applied slowly, without shock, and is held at a constant value, the resulting stress in the part is called static stress. Because σmax = σmin, the stress ratio for static stress is R =1.0

2. Repeated and reversed stress A stress reversal occurs when a given element of a load-carrying member is subjected to a certain level of tensile stress followed by the same level of compressive stress. The stress is called repeated and reversed. Because σ min = - σmax, the stress ratio is R = -1.0, and the mean stress is zero.

3. Fluctuating stress When a load-carrying member is subjected to an alternating stress with a Non zero mean, the loading produces fluctuating stress.

4. Shock , Impact and Random loading Loads applied suddenly and rapidly cause shock or impact. Examples include a hammer blow, a weight falling onto a structure, and the action inside a rock crusher. When varying loads are applied that are not regular in their amplitude, the loading is called random. However, here we can categorize them as two types of loading viz. static loading and variable loading. A static load is a stationary force or couple applied to a member. To be stationary the force or couple must be unchanging in magnitude, point or points of application and direction. A static load can produce axial tension or compression, a shear load, a bending load, a torsional load or the combination of these. Under the static loading, the ductile material undergoes elastic elongation following Hook’s law until it reaches the yield point. The ductile material regains original shape when the load is removed until this point. The initial linear portion of the curve (OA) is the elastic region. Point A is the elastic limit (the greatest stress that the metal can withstand without

undergone permanent or plastic deformation. ‘A’ is the proportional limit where the curve deviates from linearity and The slope of the linear portion is the modulus of elasticity “E”. Point ‘B’ is the yield strength, defined as the stress which will produce a small amount of strain equal to 0.002 (OC). Beyond this point, the ratio of stress and strain is not linear and the material undergoes plastic deformation. As the plastic deformation increases, the metal becomes stronger (strain hardening) until reaching the maximum load, giving ultimate tensile strength ‘D’. When the loading is continued beyond the ultimate stress, the cross-sectional area decreases rapidly in a localized region of the test specimen which is known as “necking”. Since the cross-sectional area decreases, the load carrying capacity of this region also decreases rapidly. The load (and stress) keeps dropping until the specimen reaches the fracture point and finally the material fails.

However, in case of brittle material there will be neither yielding, nor strain hardening or necking. There is no appreciable plastic deformation. Crack propagates nearly perpendicular to the direction of the applied stress by cleavage – breaking of atomic bonds along specific crystallographic planes (cleavage planes). Crack propagation is very fast and so the brittle material fails without giving any sign which is an important drawback of brittle material. However, some brittle metals such as cast iron show small amounts of plasticity before failure.

Generally, the condition frequently arises, however, in which the stresses vary or they fluctuate between the levels. For example, a particular fiber on the surface of a rotating shaft subjected to the action of bending loads undergoes both tension and compression for each revolution of the shaft. If, in addition, the shaft is also axially loaded, an axial component of stress is also superposed upon the bending component. In this case, some stress is always present in any one fiber, but now the level of stress is fluctuating. These and other kinds of loading occurring in the machine members produce stresses which are called variable, repeated, alternating or fluctuating stresses. Often, machine members are found to have failed under the action of repeated or fluctuating stresses and it is found that the actual maximum stresses were below the ultimate strength of material and quite frequently much below the yield strength. The most distinguishing characteristics of these failures is that the stress have been repeated a very large number of times. Hence the failure is called fatigue failure. Fatigue failure is brittle-like (relatively little plastic deformation) - even in normally ductile materials and thus sudden and catastrophic! Fatigue failure proceeds in three distinct stages: 1. Crack initiation in the areas of stress concentration (near stress raisers) 2. Incremental crack propagation 3. Final rapid crack propagation after crack reaches critical size and ultimate catastrophic failure. Under cyclic loading, the endurance limit is used to represent the strength. It is the stress level that a material can survive for a given number of cycles of loading. Endurance strengths are usually charted on a graph called an S-N diagram.

Hence, it’s the job of the designer and engineers to know behavior of different material on different loading condition and choose the appropriate material according to the nature of the job to be performed by the design.