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MECHANICS OF MATERIALS - II

MECHANICS OF MATERIALS - II. FATIGUE – CRACK INITATION AND GROWTH MECHANISMS.

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MECHANICS OF MATERIALS - II

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  1. MECHANICS OF MATERIALS - II

  2. FATIGUE – CRACK INITATION AND GROWTH MECHANISMS

  3. IN MANY TYPES OF SERVICE APPLICATIONS METAL PARTS SUBJECTED TO REPETITIVE OF CYCLIC STRESS WILL FAIL DUE TO FATIGUE LOADING AT MUCH LOWER STRESS THAN THAT WHICH THE PART CAN WITHSTAND UNDER APPLICATIO OF A SINGLE STATIC STRESS. THE FAILURES THAT OCCUR UNDER REPEATED OR CYCLIC LOADING ARE CALLED FATIGUE FAILURES. FATIGUE HAS BECOME PREGRESSIVELY MORE PREVALENT AS TECHNOLOGY HAS DEVELOPED. A FATIGUE FAILURE IS PARTICULARLY INSIDIOUS BECAUSE IT OCCURS WITHOUT ANY OBVIOUS WARNING. FATIGUE RESULTS IN A BRITTLE-APPEARING FRACTURE, WITH NO GROSS DEFORMATION AT THE FRACTURE. FATIGUE PROCESS – AN INTRODUCTION

  4. EXAMPLES OF MACHINE PARTS IN WHICH FATIGUE FAILURES ARE COMMON, ARE MOVING PARTS SUCH AS SHAFTS, CONNECTING RODS, AND GEARS. ABOUT 80% OF FAILURES OF MACHINE PARTS ARE DUE TO FATIGUE FAILURES. A FATIGUE FAILURE USUALLY ORIGINATES AT A POINT OF STRESS CONCENTRATION SUCH AS A SHARP CORNER OR NOTCH OR AT A METALLURGICAL INCLUSION OR FLAW. ONCE NUCLEATED, THE CRACK PROPAGATES THROUGH DIFFERENT STAGES ACROSS THE WHOLE PART UNDER CYCLIC LOADING TILL THE FAILURE TAKES PLACE. IN REPEATED OR CYCLIC STRESSES MAXIMUM AND MINIMUM STRESSES ARE EQUAL, MAY BE BOTH TENSILE OR MAY BE TENSILE AND COMPRESSIVE AS IN FULLY REVERSED BENDING CASE.

  5. REPEATED OR FLUCTUATING STRESS CYCLES ARE CHARACTERIZED BY FOLLOWING NUMBER OF PARAMETERS: MEAN STRESS = MAX. STRESS + MIN. STRESS/2 RANGE OF STRESS = MAX. STRESS – MIN. STRESS STRESS AMPLITUDE = MAX. STRESS–MIN. STRESS/2 STRESS RATIO = R = MIN. STRESS / MAX. STRESS

  6. THE BASIC METHOD OF PRESENTING ENGINEERING FATIGUE DATA IS BY MEANS OF THE S – N CURVE. IN FACT IT IS A PLOT OF STRESS (S) AGAINST THE NUMBER OF CYCLES (N). THE STRESS VALUES ARE USUALLY NOMINAL STRESSES AND NUMBER OF CYCLES ARE PLOTTED ON A LOG SCALE. MOST OF THE DETERMINATION OF FATIGUE PROPERTIES OF MATERIALS HAVE BEEN MADE UNDER FULLY REVERSED BENDING PROCESS AS THE MEAN STRESS IS ZERO. S – N CURVES ARE MAINLY CONCERNED WITH FATIGUE AT HIGH NUMBER OF CYCLES (N > 10⁵ CYCLES). UNDER THESE CONDITIONS STRESS IS IN THE ELASTIC RANGE. S – N CURVES

  7. AT HIGHER VALUES OF STRESSES THE FATIGUE LIFE IS PROGRESSIVELY DECREASED, AND HENCE THIS TYPE OF FATIGUE IS CALLED LOW CYCLE FATIGUE. FOR LOW-CYCLE FATIGUE (N < 10⁴) TESTS ARE CONDUCTED WITH CONTROLLED CYCLES OF ELASTIC PLUS PLASTIC STRAIN INSTEAD OF CONTROLLED LOAD OR STRESS CYCLES. THIS IS QUITE UNDERSTANDABLE THAT THE NUMBER OF CYCLES OF STRESS WHICH A METAL CAN ENDURE BEFORE FAILURE INCREASES WITH DECREASING STRESS. THEREFORE, “N” IS TAKEN AS THE NUMBER OF CYCLES OF STRESS TO CAUSE COMPLETE FRACTURE OF THE SPECIMEN. FTIGUE TESTS AT LOW STRESSES ARE USUALLY CARRIED OUT FOR 10 ⁷ OR MORE CYCLES.

  8. FOR A FEW ENGINEERING MATERIALS, THE S-N CURVES BECOMES HORIZONTAL AT A CERTAIN LIMITING STRESS VALUES. BELOW THIS LIMIT MATERIAL WILL NEVER FAIL. THIS LIMITING VALUE IS CALLED FATIGUE OR ENDURANCE LIMIT. HOWEVER, MOST OF THE NON-FERROUS MATERIALS DO NOT HAVE A TRUE FATIGUE LIMIT AS THE CURVES DO NOT BECOME HORIZONTAL. THE S-N CURVR IN THE HIGH CYCLE MAY BE DESCRIBED BY THE BASQUIN EQUATION AS FOLLOWS: N (σa)p = C WHERE “σa” IS THE AMPLITUDE OF STRESS AND “p” AND “C” ARE THE EMPIRICAL CONSTANTS.

  9. THE USUAL PROCEDURE FOR DETERMINING AND S-N CURVE IS TO TEST THE FIRST SPECIMEN AT A HIGH STRESS WHERE THE FAILURE IS EXPECTED IN A FARILY SHORT NUMBER OF CYCLES, AT ABOUT 2/3 OF THE STATIC TENSILE STRENGTH OF THE MATERIAL. THE TEST STRESS IS DECREASED FOR EACH SUCCEEDING SPECIMEN UNTIL ONE OR TWO SPECIMENS DO NOT FAIL IN THE SPECIFIED NUMBER OF CYCLE, WHICH IS USUALLY AT LEAST 10⁷ CYCLES. THE HIGHEST STRESS AT WHICH A NON-FAILURE OF SPECIMEN IS OBTAINED IS TAKEN AS THE FAILURE LIMIT. FOR MATERIALS WITHOUT A FATIGUE LIMIT, THE TEST IS USUALLY TERMINATED FOR PRACTICAL CONSIDERATIONS AT A LOW STRESS WHERE THE LIFE IS ABOUT 10⁸ OR 5 X10⁸ CYCLES.

  10. THE S-N CURVE IS USUALLY DETERMINED WITH ABOUT 8 TO 12 SPECIMENS. IT WOULD GENERALLY BE FOUND THAT THERE IS CONSIDERABLE AMOUNT OF SCATTER IN THE RESULTS. BUT A SMOTTH CURVE CAN USUALLY BE DRAWN THROUGH THE POINTS WITHOUT TOO MUCH DIFFICULTY AN ERROR.

  11. HISTORICALLY FATIGUE STUDIES HAVE BEEN CONCERNED WITH CONDITIONS OF SERVICE IN WHICH FAILURE OCCURRED AT MORE THAN 10⁴ CYCLES OF STRESS. HOWEVER, THERE IS GROWING RECOGNITION OF ENGINEERING FAILURES WHICH OCCUR AT RELATIVELY HIGH STRESS AND LOW NUMBER OF CYCLES TO FAILURE. THIS TYPE OF FATIGUE MUST BE CONSIDERED IN THE DESIGN OF NUCLEAR PRESSURE VESSELS, STEAM TURBINES, AND MOST OTHER TYPES OF POWER MACHINERY. LOW-CYCLE FATIGUE CONDITIONS FREQUENTLY ARE CREATED WHERE THE REPEATED STRESSES ARE OF THERMAL ORIGIN. LOW-CYCLE FATIGUE

  12. LOW-CYCLE FATIGUE CONDITIONS FREQUENTLY ARE CREATED WHERE THE REPEATED STRESSES ARE OF THERMAL ORIGIN. SINCE THERMAL STRESSES ARISE FROM THE THERMAL EXPANSION OF THE MATERIALS, IT IS EASY TO SEE THAT IN THIS CASE FATIGUE RESULTS FROM CYCLIC STRAIN RATHER THAN FROM CYCLIC STRESS. THE USUAL WAY OF PRESENTING LOW-CYCLE FATIGUE TEST RESULTS IS TO PLOT THE PLASTIC STRAIN RANGE AGAINST NUMBER OF CYCLES. A STRAING LINE MAY BE OBTAINED WHEN PLOTTED ON LOG-LOG COORDINATES.

  13. THIS TYPE OF BEHAVIOUR IS KNOWN AS THE COFFIN-MANSON RELATION, WHICH IS BEST DESCRIBED BY: ∆εp/2 = εf (2N)c WHERE ∆εp/2 IS PLASTIC STRAIN AMPLITUDE, εf IS THE FATIGUE DUCTILITY COEFFICIENT AND IS EQUAL TO THE TRUE FRACTURE STRAIN FOR MANY METALS, AND “c” IS FATIGUE DUCTILITY EXPONENT.

  14. GENERALLY, FATIGUE FAILURE MECHANISM CONSISTS OF FOLLOWING TWO MAINPROCESSES: CRACK INITIATION CRACK PROPAGATION CRACK PROPAGATION PROCESS CONSISTS OF FOLLOWING THREE STAGES: STAGE I CRACK GROWTH STAGE II CRACK GROWTH STAGE III CRACK GROWH CRACKS USUALLY INITIATE FROM STRESS CONCENTRATION POINTS THAT MAY INCLUDE MANY ENGINEERING, MANUFACTURING AND METALLURGICAL PARAMETERS. STAGES OF FATIGUE PROCESS

  15. CRACK INITATION DOES NOT TAKE MUCH TIME IN THE PRESENCE OF STRESS CONCENTRATION POINTS. ONCE THE CRACKS ARE INITIATED THEY STARTED TO GROW. IN STAGE I CRACK GROWTH IS VERY LOW AND CAN BE AVOID WITH STRENGTHENING OF MATERIALS. STAGE I CRACK GROWTH IS MARKED BY PSBs. STAGE II CRACK GROWTH COVERS MUCH OF THE LIFE OF MACHINE AND STRUCTURAL COMPONENTS. IN THIS REGION CRACK GROWS RAPIDLY AND FATIGUE STRIATIONS ARE CREATED AS CRACK ADVANCES ACROSS THE X-SECTION OF THE SPECIMEN.

  16. IN STAGE III CRACKS COVER A SUFFICIENT AREA SO THAT THE REMAINING METAL AT THE X-SECTION CAN NOT SUPPORT THE APPLIED LOAD AND CONSEQUENTLY SPECIMEN FAILS. THIS REGION OF CRACK GROWTH COVERS SMALL PART OF SPECIMEN LIFE. THE RELATIVE PROPORTION OF THE TOTAL CYCLES TO FAILURE THAT ARE INVOLVED WITH EACH STAGE DEPENDS ON THE TEST CONDITIONS AND THE MATERIAL. HOWEVER, IT IS WELL ESTABLISHED THAT A FATIGUE CRACK CAN BE FORMED BERFORE 10% OF THE TOTAL LIFE OF THE SPECIMEN HAS ELASPED. IN GENERAL TERMS THE LARGER PROPORTION OF THE TOTAL LIFE IS CONSUMED BY THE STAGE II CRACK GROWTH WHILE STAGE I AND STAGE III CRACKS COMSUME COMPARATIVELY SMALL PROPORTIONS OF TOTAL LIFE.

  17. CRACK GROWTH RATE (da/dN) IS IN FACT THE FUNCTION OF STRESS AND CRACK LENGTH WHICH THE FATIGUE CRACK GROWTH RATE VARIES WITH THE VARIATION OF APPLIED CYCLIC STRESS AND TH CRACK LENGTH. FOR MANY ENGINEERING MATERIALS AND ALLOYS THE FATIGUE CRACK GROWTH RATE CAN BE EXPRESSED BY THE FOLLOWING RELATIONSHIP: da/dN = A (∆K)m WHERE “∆K” IS STRESS INTESITY FACTOR RANGE WHICH DEPENDS UPON GEOMETRY OF THE NOTCH. (STRESS √∆Πa) A & m ARE THE MATERIAL CONSTANTS AND DEPEND UPON ENVIRONMENT, FREQUENCY, TEMPERATURE AND STRESS RATIO. USUALLY FATIGUE CRACK LENGTH VERSUS STRESS-INTENSITY FACTOR RANGE DATA ARE PLOTTED AS log da/dN VERSUS log ∆K. THESE DATA ARE PLOTTED AS A log-log PLOT SINCE IN MOST CASES A STRIAGHT LINE CLOSE TO A STRAIGHT-LINE PLOT IS OBTAINED.

  18. FATIGUE LIFE CALCULATION FATIGUE LIFE OF COMPONENTS / STRUCTURES CAN BE CALCULATED BY INTEGRATING THE PREVIOUSLY MENTIONED EQUATION, (da/dN = A ∆Km). WE KNOW THAT ∆K = Yσ√∏a, THEREFORE, da/dN = A ∆Km = A(Yσ√∏a)m ∫da = A(Yσ√∏a)m ∫ dN ABOVE EQUATION WOULD BE INTEGRATED BETWEEN AN INITIAL CRACK (FLAW) SIZE a0 AND THE CRITICAL CRACK (FLAW) SIZE af, WHICH IS PRODUCED AT FATIGUE FAILURE AFTER THE NUMBER OF CYCLES TO FAILURE Nf.

  19. ONE MAY CONCLUDE THAT FATIGUE CRACK GROWTH RATE IS LOW IN CASE OF SMALL CRACK LENGTH. CRACK GROWTH RATE INCREASES WITH INCREASING CRACK LENGTH. AN INCREAS IN THE CYCLIC STRESS INCREASES THE CRACK GROWTH RATE. FATIGUE LIFE TIME DATA IS PLOTTED AS S-N CURVES IN WHICH THE STRESS “S” TO CAUSE FAILURE IS PLOTTED AGAINST THE NUMBER OF CYCLES “N” AT WHICH FAILURE OCCURS. THE HORIZONTAL PART OF THE SN PLOT DEFINES THE FATIGUE OR ENDURANCE LIMIT AND LIES BETWEEN 106 TO1010 CYCLES.

  20. MANY FERROUS ALLOYS EXHIBIT AN ENDURANCE LIMIT THAT IS ABOUT ONE-HALF OF THEIR TENSILE STENGTH. NON-FERROUS ALLOYS SUCH AS ALUMINUM ALLOYS MAY FATIGUE STRENGTHS AS LOW AS ONE-THIRD OF THEIR TENSILE STRENGTH. FATIGUE LIFE OF COMPONENTS IS AFFECTED BY ONE OF THE FOLLOWING FACTORS: STRESS CONCENTRATION SURFACE ROUGHNESS SURFACE CONDITION ENVIRONMENT FINALLY FATIGUE IS ONE OF THE MAIN CAUSE OF ALL TYPES OF INDUSTRIAL FAILURE AND, THEREFORE, MUST BE AVOIDED BY CAREFULL ANALYSIS OF SERVICE CONDITIONS.

  21. CREEP AND STRESS RUPTURE OF METALS CREEP IS THE CONTINUED SLOW STRAINING OF A MATERIAL UNDER THE INFLUENCE OF A CONSTANT LOAD. THE AMOUNT OF STRAIN DEVELOPED IN A MATERIAL BECOMES A FUNCTION OF TIME AND TEMPERATURE, AS WELL AS OF STRESS. THE CREEP OF METALS AND ALLOYS IS VERY IMPORTANT FOR SOME TYPES OF DENGINEERING DESIGNS, PARTICULARLY THOSE OPERATING AT ELEVATED TEMPERATURES. FOR MANY ENGINEERING DESIGNS OPERATING AT ELEVATED TEMPERATURS, THE CREEP OF MATERIALS IS THE LIMITING FACTOR WITH RESPECT TO HOW HIGH THE OPERATING TEMPERATURE MIGHT BE.

  22. THE PHENOMENON OF CREEP CAN OCCUR IN ALL TYPES OF MATERIALS BUT THERE IS A THRESHOLD TEMPERATURE BELOW WHICH CREEP DOSE NOT BECOME A FACTOR IN STRESS-STRAIN RELATIONSHIPS. IN CASE OF THERMOPLASTIC MATERIALS, CREEP IS OF SIGNIFICANT AT ALL TEMPERATURES JUST ABOVE MELTING TEMPERATURES. IN METALS AND CERAMICS , CREEP IS CONSIDERED AS A HIGH TEMPERATURE PHENOMENON, ALTHOUGH LEAD CREEPS AT ROOM TEMPERATURE, AND OCCURS AT TEMPERATURES ABOVE 0.3 – 0.4 IN METALS AND ABOVE 0.4 - 0.5 OF MELTING TEMPERATURE IN CERAMICS.

  23. THERE ARE THREE STAGES OF A TYPICAL CREEP CURVE OF STRAIN AGAINST TIME AT CONSTANT STRESS. THESE ARE PRIMARY OR TRANSIENT CREEP, SECONDARY OR STEADY-STATE CREEP, AND TERTIARY CREEP. IN THE FIRST PHASE THERE IS FIRST AN INSTANTANEOUS, RAPID ELONGATION OF THE MATERIAL. FOLLOWING THIS THE MATERIAL EXHIBITS PRIMARY CREEP IN WHICH THE STRAIN RATE DECREASES WITH TIME. DURING PRIMARY CREEP THE CREEP RATE PROGRESSIVELY DECREASES WITH TIME. AFTER THIS IN SECONDARY STAGE OF CREEP OCCURS IN WHICH THE CREEP RATE IS ESSENTIALLY CONSTANT. FINALLY, THE TERTIARY STAGE OF CREEP OCCURS IN WHICH THE CREEP RATE RAPIDLY INCREASES WITH TIME UP TO THE STRAIN AT FRACTURE.

  24. HIGHER STRESSES AND HIGHER TEMPERATURES INCREASE THE CREEP RATE OF MATERIALS. AT LOW TEMPERATURES AND LOW STRESSES, METALS SHOW PRIMARY CREEP BUT NEGLIGIBLE SECONDARY CREEP. ITHE EFFECTS OF TEMPERATURES AND STRESS ON THE CREEP RATE AE DETERMINED BY THE CREEP MULTIPLE TESTS. THESE TESTS ARE RUN USING DIFFERENT STRESS LEVELS AT CONSTANT TEMPERATURE OF DIFFERENT TEMPERATURES AT CONSTANT STRESS, AND STRESS CURVES ARE PLOTTED.

  25. QUESTIONS AND QUERIES IF ANY! IF NOT THEN GOOD BYE SEE ALL OF YOU IN NEXT LECTURE ON-------------------------

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