DESIGN CONCEPTS & M/C DRAWING

ME-309 DME-I

Prepared By:Prof. Ketul Brahmbhatt

STRESS CONCENTRATIONThis irregularity in the stress distribution

caused by abrupt changes of form is called stress concentration. It occurs for all kinds of stresses in the presence of fillets, notches, holes, keyways, splines, surface roughness or scratches etc.

Theoretical Stress Concentration Factor:-The theoretical or form stress concentration factor is defined as the ratio of the maximum stress in a member (at a notch or a fillet) to the nominal stress at the same section based upon net area. Mathematically, theoretical or form stress concentration factor,

Kt=

Highest Value of actual stress near discontinuityNominal stress obtained by elementary equations for minimum cross-section

SCF at Hole

CAUSES OF SCF:-

I. Variation in Material Properties

II. Load Application

III. Abrupt change in section

IV. Discontinuities in the components

V. Machining Scratches

d / b = 0.212/60=0.2From Std Table Kt=2.5D / d = 50/25=2r/d=5/25=0.2From Std Table Kt=1.64

METHODS OF REDUCING STRESS CONCENTRATION

A. Additional notches and HolesB. Fillet radius, Undercutting and

notches for member in bendingC. Drilling Holes for Shaft

WHAT IS FATIGUE?

Fatigue is a phenomenon associated with variable loading or more precisely to cyclic stressing or straining of a material. Just as we human beings get fatigue when a specific task is repeatedly performed, in a similar manner metallic components subjected to variable loading get fatigue, which leads to their premature failure under specific conditions.

In reality most mechanical components experience variable loading due to -Change in the magnitude of applied load punching or shearing operations- -Change in direction of load application a connecting rod -Change in point of load application : a rotating shaft The worst case of fatigue loading is the case known as fully-reversible load. One cycle of this type of loading occurs when a tensile stress of some value is applied to an unloaded part and then released, then a compressive stress of the same value is applied and released.

Fatigue Failure ASTM Definition of fatigue

• The process of progressive localized permanent structural changes occurring in a material subjected to conditions that produce fluctuating stresses at some point or points and that may culminate in cracks or complete fracture after a sufficient number of fluctuations.

A fatigue failure begins with a small crack; the initial crack may be so minute and can not be detected. The crack usually develops at a point of localized stress concentration like discontinuity in the material, such as a change in cross section, a keyway or a hole. Once a crack is initiated, the stress concentration effect become greater and the crack propagates. Consequently the stressed area decreases in size, the stress increase in magnitude and the crack propagates more rapidly. Until finally, the remaining area is unable to sustain the load and the component fails suddenly. Thus fatigue loading results in sudden unwarned failure.

Fatigue Failure Stages Thus three stages are involved in fatigue failure namely -Crack initiation -Crack propagation -Fracture

Basic features of failure appearance • A fatigue failure, therefore, is characterized by two distinct regions. The first of these is due to progressive development of the crack, while the second is due to the sudden fracture. The zone of sudden fracture is very similar in appearance to the fracture of a brittle material, such as cast iron, that has failed in tension. The crack propagation zone could be distinguished from a polished appearance. A careful examination (by an experienced person) of the failed cross section could also reveal the site of crack origin

How is the fatigue strength of a metal determined?

The fatigue behavior of a specific material, heat-treated to a specific strength level, is determined by a series of laboratory tests on a large number of apparently identical samples of that specific material. These laboratory samples are now standardized in geometry and configuration such that no extraneous factors other than the applied stress influence the fatigue life. They are machined with shape characteristics which maximize the fatigue life of a metal, and are highly polished to provide the surface characteristics which enable the best fatigue life.

R.R.Moore Bending Principle:-“The machine design is based on the rotating beam principle. The specimen functions as a simple beam symmetrically loaded at two points. When rotated one half revolution, the stresses in the fibers originally below the neutral axis are reversed from tension to compression and vice versa. Upon completing the revolution, the stresses are again reversed so that during one revolution the test specimen passes through a complete cycle of flexural stress (tension and compression).”

The S-N Diagram Tests on several specimens are conducted under identical conditions with varying levels of stress amplitude. The cyclic stress level of the first set of tests is some large percentage of the Ultimate Tensile Stress (UTS), which produces failure in a relatively small number of cycles. Subsequent tests are run at lower cyclic stress values until a level is found at which the samples will survive 10 million cycles without failure. The results are plotted as an S-N diagram usually on semi-log or on log-log paper, depicting the life in number of cycles tested as a function of the stress amplitude.

Low Cycle Fatigue The body of knowledge available on fatigue failure from N=1 to N=1000 cycles is generally classified as low-cycle fatigue. High Cycle Fatigue High-cycle fatigue, then, is concerned with failure corresponding to stress cycles greater than 103 cycles.(Note that a stress cycle (N=1) constitutes a single application and removal of a load and then another application and removal of load in the opposite direction. Thus N= ½ means that the load is applied once and then removed, which is the case with the simple tensile test.)

Finite and Infinite Life We also distinguish a finite-life and an infinite-life region. Finite life region covers life in terms of number of stress reversals upto the knee point.(in case of steels) beyond which is the infinite-life region. The boundary between these regions cannot be clearly defined except for specific materials; but it lies somewhere between 106 and 107 cycles, for materials exhibiting fatigue limit.

Endurance limit- Approximate Estimatation:- (a)Surface Condition (Ka): such as: polished, ground,

machined, as-forged, corroded, etc. Surface is perhaps the most important influence on fatigue life;

(b) Size (Kb): This factor accounts for changes which occur when the actual size of the part or the cross-section differs from that of the test specimens;

(c) Reliability (Kc): This factor accounts for the scatter of test data. For example, an 8% standard deviation in the test data requires a ke value of 0.868 for 95% reliability, and 0.753 for 99.9% reliability. (d) Modifying factor of account stress concentration (Kd)(f) Miscellaneous (Ke): This factor accounts for reductions from all other effects, including residual stresses, corrosion, plating, metal spraying, fretting, and others.

Se’= endurance limit stress of a rotating beam specimen subjected to reverse bending stressSe=endurance limit of a particular mechanical components subjected to reverse bending stressKa = Surface Condition Kb= Size FactorKc= Reliability FactorKd=Modifying factor of account stress concentration Ke= Miscellaneous Factors

Size Factor Kb

Fatigue Stress Concentration The existence of irregularities or discontinuities, such as holes, grooves, or notches, in a part increase the magnitude of stresses significantly in the immediate vicinity of the discontinuity. Fatigue failure mostly originates from such places. Hence its effect must be accounted and normally a fatigue stress-concentration factor Kf is applied when designing against fatigue, even if the materials behavior is ductile.

Fatigue Stress Concentration Factor

Kd= 1/Kf

Geometric stress concentration factor Kt and Fatigue Stress Concentration factor KfThis form of definition needs that the fatigue stress concentration factor or the endurance strength values for different notch geometries on each of the material to be used should be evaluated. However once sufficient data was available a simple approach, useful at preliminary design stages was evolved to determine the fatigue stress concentration factor value from the geometrical (theoretical) stress concentration values, data charts for which is readily available, using a notch sensitivity relation.

Notch Sensitivity Notch sensitivity q is defined by the equation