1 Design for Different Type of Loading Lecture Notes Dr. Rakhmad Arief Siregar Kolej Universiti Kejuruteraan Utara Malaysia Machine Element in Mechanical Design Fourth Edition in SI Unit Robert L. Mott Chapter 5

2 Chapter 5 Design for Different Types of Loading Objectives: Identify various kinds of loading commonly encountered by machine parts, including static, repeated and reversed, fluctuating, shock or impact and random Define the term stress ratio and compute its value for the various kinds of loading Define the concept of fatigue Define the material property of endurance strength and determine estimates of its magnitude for different materials Recognize the factors that affect the magnitude of endurance strength

3 Chapter 5 Design for Different Types of Loading Objectives: Define the term design factor Specify a suitable value for the design factor Define the maximum normal stress theory of failure and the modified Mohr method for design with brittle materials Define maximum shear stress theory of failure Define he distortion energy theory, also called the von Mises theory or the Mises-Hencky theory Describe the Goodman method and apply it to the design of parts subjected to fluctuating stresses Consider statistical approaches, finite life and damage accumulation method for design

4 Types of Loading & Stress Ratio Types of loading: Static: when a part is subjected to a load that is applied slowly, without shock, and is held at constant value. Repeated and Reversed: when a part is subjected to a certain level of tensile stress followed by the same level of compressive stress Fluctuating stress: when a load-carrying member is subjected to an alternating stress with a nonzero mean. Shock or impact: loads applied suddenly and rapidly cause shock or impact, i.e., hammer blow, weight falling Random: when varying loads are applied that are not regular in their amplitude

5 Figures See Fig. 5-1 for static stress See Fig. 5-2 for repeated, reversed stress See Fig. 5-4 for Fluctuating stress

6 Impact Load Strain Gage A Strain Gage B Signal Conditioner Digital Oscilloscope Striker Bar Input BarOutput Bar V Photodiode velocity sensor (a)

7 Impact Load

8 Stress ratio Stress ratio is one of method to characterize variation of stresses. Maximum stress,  max Minimum stress,  min Mean stress,  m Alternating stress,  a (stress amplitude)

9 Photographs of failed parts Failure of a truck drive shaft spline due to corrosion fatigue

10 Photographs of failed parts Failure of a stamped steel bracket due to residual stresses

11 Photographs of failed parts Failure of an automotive drag link (steering wheel)

12 Photographs of failed parts Failure of bolt in the overhead-pulley

13 Photographs of failed parts Automotive rocker-arm articulation-joint fatigue failure

14 Photographs of failed parts Valve-spring failure caused by spring surge in an over speed engine

15 Photographs of failed parts Brittle facture of a lock washer in one-half cycle

16 Failure resulting from static loading Static loading Direct tension and compression Direct shear Torsional shear Vertical shearing stresses Bending Buckling How to predict failure if the component is subjected to combine loading?

17 Ductile materials Maximum shear stress Also known as Tresca theory The maximum shear stress hypothesis states that yielding begin “whenever the maximum shear stress in any element becomes equal to the maximum shear stress in a tension test specimen of the same material when specimen begins to yield”

18 Triaxial shear stresses The maximum shear stress graphically represented in three dimensions

19 Biaxial stress 11 22 -S y SySy SySy

20 Ductile materials Distortion energy Also known as von Misses – Hencky theory The maximum strain energy hypothesis predicts failure by yielding occurs “when distortion energy in a unit volume equals the distortion energy in the same when uniaxially stressed to the yield strength”

21 Ductile materials Distortion energy Under the name of octahedral shear stress this theory predicts failure occurs “whenever the octahedral shear stress for any stress state equal or exceeds the octahedral shear stress for the simple tension test at failure”

22 Triaxial stress 33 22 11 The distortion energy theory graphically represented in three dimensions

23 Biaxial stress 11 22 SySy SySy -S y

24 Problem 1 A hot-rolled steel is subjected to principle stress  1 = 210 MPa,  1 = 480 MPa and  3 = 0 MPa. By utilizing UTM the hot-rolled steel has a yield strength of S yt =S yc = 690 MPa and a true strain at fracture of  f = Estimate the factor of safety.

25 Solution Maximum shear stress theory Distortion energy theory

26 Brittle materials Maximum normal stress Also known as Rankine theory The maximum normal stress hypothesis predicts failure occurs “whenever one of the three principle stresses equals or exceeds the strength” Suppose we arrange:  1 >  2 >  3 Note: n = safety factor

27 Brittle materials Modification of Mohr Coulomb-Mohr Mod. I-Mohr

28 Brittle materials Modification of Mohr Mod. II-Mohr

29 Problem 2 A cast iron is subjected to principle stress  1 = 210 MPa,  1 = 480 MPa and  3 = 0 MPa. By utilizing UTM the cast iron has a yield strength of S ut =215 MPa and S uc = 750 MPa. Estimate the factor of safety by using: (1) Coulomb-Mohr failure model (2) Mod. I-Mohr failure model (3) Mod. II-Mohr failure model

30 Solution Maximum shear stress theory Distortion energy theory

31 Fatigue A machine components often subjected to dynamic loading such as: variable, repeated alternating or fluctuating stresses. In most cases machine members are found to have failed under the action of repeated or fluctuating stresses. The analysis reveals that the actual maximum stresses were below the ultimate strength of the material and quite frequently even below the yield stress

32 Fatigue This kind failure CAN NOT be detected by naked eye and even quite difficult to locate in a Magnaflux or X-ray inspection This failure called as fatigue failure. Begins with a small crack and develops a point of discontinuity in materials such as change in cross section, a keyway or a hole. Once developed, the stress-concentration effect becomes greater and crack progresses more rapidly

33 Endurance strength Endurance strength of material is its ability to withstand fatigue loads. Endurance strengths are usually charted on a graph like shown in Fig. 5-7, called as S-N diagram. Factors affecting endurance strength: Surface finish Material factor Type of stress factor Reliability Factor Size Factor