英漢雙語材料力學14PPT學習教案

1、會計學1第1頁/共66頁141 SUMMARY142 SOME NOMENCLATURE IN THE ALTERNATING STRESS143 ENDURANCE LIMIT OF A MATERIALS AND ITS TEST144 ENDURANCE LIMIT OF A MEMBER AND ITS CALCULATION145 CALCULATION OF THE FATIGUE STRENGTH OF THE MEMBER UNDER SYMMETRIC CYCLES146 SIMPLE INTRODUCTION OF MECHANICAL PROPERTIES OF MATE

2、RIALS AT NON-CONSTANT TEMPERATURES AND STATIC LOADS第2頁/共66頁141 概述概述142 交變應力的幾個名詞術語交變應力的幾個名詞術語143 材料持久限及其測定材料持久限及其測定144 構件持久限及其計算構件持久限及其計算145 對稱循環(huán)下對稱循環(huán)下構件的疲勞強度計算構件的疲勞強度計算146 非常溫靜載下材料力學性能簡介非常溫靜載下材料力學性能簡介第3頁/共66頁1、Alternating stress：Stress at a point inside a member is changing periodically with time.

3、This kind of stress is called the alternating stress.Fold iron threadPPPPhigh-pressure oilLow-pressure oil第4頁/共66頁一、交變應力一、交變應力：構件內一點處的應力隨時間作周期性變化，這 種應力稱為交變應力。折鐵絲折鐵絲PPPP第5頁/共66頁2、Developing process of the fatigue failure: :1).Sub-structures and microscopic structures produce changes and the core of t

4、he permanent damage is formed.2).Microcosmic cracks are produced.3).Microcosmic cracks expand 、 merge and form the“l(fā)eading” crack.4).The macroscopic “l(fā)eading” crack expand steadily.5).The structure losts its stability or ruptures completely. Failure of materials under the action of an alternating st

5、ress, in custom, is called the fatigue failure. 第6頁/共66頁二、疲勞破壞的發(fā)展過程二、疲勞破壞的發(fā)展過程: :1.亞結構和顯微結構發(fā)生變化，從而永久損傷形核。2.產生微觀裂紋。3.微觀裂紋長大并合并，形成“主導”裂紋。4.宏觀主導裂紋穩(wěn)定擴展。5.結構失穩(wěn)或完全斷裂。材料在交變應力下的破壞，習慣上稱為疲勞破壞。第7頁/共66頁3、Characteristics of the fatigue failure:. ).1jxwork2).The happening of rupture needs some numbers of cycling.

6、3).The failure is of the brittle rupture.4).The rupture area shows obviously different zones. （Smooth zone and coarse zone）第8頁/共66頁三、疲勞破壞的特點三、疲勞破壞的特點: :2.斷裂發(fā)生要經過一定的循環(huán)次數。3.破壞均呈脆斷。4.“斷口”分區(qū)明顯。 （光滑區(qū)和粗糙區(qū)）jx工作 . 1。第9頁/共66頁142 SOME NOMENCLATURE IN THE ALTERNATING STRESS1、Cycle characteristics：)( ; )( ; min

7、maxminmaxmaxminmaxminr3、Amplitude of stress：2minmaxa2、Mean stress：2minmaxmmminmaxaTto第10頁/共66頁142 交變應力的幾個名詞術語交變應力的幾個名詞術語一、循環(huán)特征：一、循環(huán)特征：)( ; )( ; minmaxminmaxmaxminmaxminr三、應力幅：三、應力幅：2minmaxa二、平均應力：二、平均應力：2minmaxmmminmaxaTto第11頁/共66頁mt4、Several special alternating stresses：1).Symmetric cycle：1maxminrm

8、axa0mminmaxaTo第12頁/共66頁mt四、幾種特殊的交變應力：四、幾種特殊的交變應力：1.對稱循環(huán)：1maxminrmaxa0mminmaxaTo第13頁/共66頁t2).Fluctuating cycle：0maxminr2maxma3).Static cycle：1maxminr0amaxm5、Stable alternating stress：cycle characteristics and the cycle period are not changed.minmaxatmmminmaxminoo第14頁/共66頁t2.脈動循環(huán)：0maxminr2maxma3.靜循環(huán)：1

9、maxminr0amaxm五、穩(wěn)定交變應力：循環(huán)特征及周期不變。五、穩(wěn)定交變應力：循環(huán)特征及周期不變。minmaxatmmminmaxminoo第15頁/共66頁MPa5610115. 05830042maxmaxAPMPa2 .5370115. 05580042minminAPMPa1225375612minmaxaMPa54925375612minmaxm957. 0561537maxminr Example 1 A bolt connected the connecting with rod in a generator is subjected to the maximum tensi

10、le force in work Pmax =58.3kN，the minimum tensile force is Pmin =55.8kN. Inside diameter of the whorl is d=11.5mm，try to determine a 、m and r.Solution：第16頁/共66頁MPa5610115. 05830042maxmaxAPMPa2 .5370115. 05580042minminAPMPa1225375612minmaxaMPa54925375612minmaxm957. 0561537maxminr 例例1 1 發(fā)動機連桿大頭螺釘工作時最大

11、拉力Pmax =58.3kN，最小拉力Pmin =55.8kN ，螺紋內徑為 d=11.5mm，試求 a 、m 和 r。解：第17頁/共66頁143 ENDURANCE LIMIT OF A MATERIAL AND ITS TEST1、Endurance limit (fatigue limit)of a materials： As long as the maximum stress of the cycle stress does not exceed a“the maximum limit”, a material may be subjected to millions of tim

12、es cycling without fatigue. This maximum stress is called the “fatigue limit”. It is designated by r .2 2、 N curve（Stresslife curve）：N0cycle baserEndurance limit of materialsANominal endurance limit N(cycling numbers)NAArN0o第18頁/共66頁143 材料持久限及其測定材料持久限及其測定一、材料持久限一、材料持久限( (疲勞極限疲勞極限) )： 循環(huán)應力中的最大只要不超過某個

13、“最大限度”,構件就可以經歷無數次循環(huán)而不發(fā)生疲勞破壞，這個限度值稱為“疲勞極限”，用r 表示。二、二、 N 曲線（應力曲線（應力壽命曲線）：壽命曲線）：N0循環(huán)基數。r材料持久限。A名義持久限。N(循環(huán)次數)NAArN0o第19頁/共66頁144 ENDURANCE LIMIT OF A MEMBER AND ITS CALCULATION1、Endurance limit of a material r 0 The relation between r0 and r ：1). K Effective stress- concentration coefficient：2). Size co

14、efficient：rrK0rr)(Endurance limit of the smooth specimen with larger dimensionsEndurance limit of the small smooth specimen =krdr)()(Endurance limit of the smooth specimen without stress concentration Endurance limit of the same-dimension specimen with stress concentrationK =第20頁/共66頁144 構件持久限及其計算構件

15、持久限及其計算一、構件持久限一、構件持久限 r 0 r0 與 r 的關系：1. K 有效應力集中系數：krdrK)()(件的持久限同尺寸有應力集中的試的持久限無應力集中的光滑試件2. 尺寸系數：rr)(光滑小試件的持久限限大尺寸光滑試件的持久rrK0第21頁/共66頁3). Surface quality coefficient： If the cycle stress is the shearing stress, we can change the normal stress in above formula by the shearing stress. Under the case o

16、f a symmetric cycle, r = -1. All the above coefficients can be obtained by looking up tables.rrK0drr)()(Endurance limit of the smooth specimenEndurance limit of the member =第22頁/共66頁3. 表面質量系數：drr)()(光滑試件持久限構件持久限 如果循環(huán)應力為剪應力，將上述公式中的正應力換為剪應力即可。 對稱循環(huán)下 ，r= -1 。上述各系數均可查表而得。rrK0第23頁/共66頁Example 2 A stepped

17、 shaft is shown in the figure. The material is the alloy steel of chrominium and nickl.Knowing b=920MPa，1= 420MPa and 1= 250MPa .Try to determine the effective stress-concentration coefficient and the dimension coefficient of the shaft respectively in bending and torsion.Solution：1. Coefficients of

18、the effective stress-concentration and the dimension in bending.25. 14050dD125. 0405dr55. 1, MPa1000:KAsbLooking up the figure and table we can get the effective coefficient of the stress concentration.55. 1,MPa900:sKAb55. 1,MPa920:sKAb77. 0Looking up the table we get the dimension coefficient.f50f4

19、0r=5第24頁/共66頁 例例2 階梯軸如圖，材料為鉻鎳合金鋼，b=920MPa，1= 420MPa ，1= 250MPa ，分別求出彎曲和扭轉時的有效應力集中系數和尺寸系數。解：1.彎曲時的有效應力集中系數和尺寸系數25. 14050dD125. 0405dr55. 1, MPa1000:Kb時當由圖表查有效應力集中系數55. 1, MPa900:Kb時當55. 1, MPa920:Kb時當77. 0由表查尺寸系數f50f40r=5第25頁/共66頁26. 1)900920(90010025. 128. 125. 1K81. 02. Coefficients of the effectiv

20、e stress concentration and the dimension in torsion.Looking up the figure and table we can get the effective coefficient of stress concentration.Looking up the table we get the dimension coefficient28. 1 ,MPa1000KbAs25. 1 MPa900Kb，AsWe use the rectilinear interpolation method and get ，MPa920bAs第26頁/

21、共66頁28. 1 , MPa1000:Kb時當25. 1 MPa900:Kb時，當，時當 MPa920:b26. 1)900920(90010025. 128. 125. 1K81. 02.扭轉時的有效應力集中系數和尺寸系數由圖表查有效應力集中系數應用直線插值法由表查尺寸系數第27頁/共66頁145 CALCULATION OF THE FATIGUE STRENGTH OF THE MEMBER UNDER SYMMETRIC CIRCLES1、The permissible stress of fatigue under symmetric cycles:1011 1Knn2、The s

22、trength condition of fatigue under symmetric cycles:1max第28頁/共66頁145 對稱循環(huán)下對稱循環(huán)下構件的疲勞強度計算構件的疲勞強度計算一、一、對稱循環(huán)的對稱循環(huán)的疲勞許用應力疲勞許用應力: :1011 1Knn二、二、對稱循環(huán)的對稱循環(huán)的疲勞強度條件疲勞強度條件: :1max第29頁/共66頁 SolutionminmaxWMMPa2 .6505. 03280031maxminrIt is the symmetric cycle.f70f50r=7.5MM Example Example 3 A constant force coup

23、le M=0.8kNm is acted on a rotating carbon-steel shaft. The surface of the shaft is of finish turning. Knowing b=600MPa，1= 250MPa and n=1.9. Try to check the strength of the shaft.第30頁/共66頁 例例3 旋轉碳鋼軸上，作用一不變的力偶 M=0.8kNm，軸表面經過精車， b=600MPa，1= 250MPa，規(guī)定 n=1.9，試校核軸的強度。解確定危險點應力及循環(huán) 特征minmaxWMMPa2 .6505. 032

24、80031maxminr為對稱循環(huán)f70f50r=7.5MM第31頁/共66頁1max MPa600 ; 15. 0 ; 4 . 1 bdrdDDetermine K：Determine ：From the figure we getLooking up the figure we get 4 . 1K79. 0Determine ：the surface is of finish turning， =0.94MPa8 .692504 . 19 . 194. 079. 0 11011KnnSafe 第32頁/共66頁強度校核1max 查圖表求各影響系數，計算構件持久限。MPa600 ; 15.

25、 0 ; 4 . 1 bdrdD求K：求 ：查圖得查圖得4 . 1K79. 0求 ：表面精車， =0.94MPa8 .692504 . 19 . 194. 079. 0 11011Knn安全第33頁/共66頁146 SIMPLE INTRODUCTION OF MECHANICAL PROPERTIES OF MATERIALS AT NON-CONSTANT TEMPERATURES AND STATIC LOADS1、Effect of the stress rate on mechanical properties of materials.dtdLow-carbon steelO1St

26、atic load2Dynamic loadRelation between the stress rate and the yield limit0 20 40 60 80 100320300280260240220200s (MPa) (MPa/s) 3the load is called the dynamic load.As第34頁/共66頁146 非常溫靜載下材料力學性能簡介非常溫靜載下材料力學性能簡介一、應力速率對材料力學性能的影響一、應力速率對材料力學性能的影響dtd時稱為動載 3低碳鋼O1靜荷載2動荷載應力速率與屈服極限的關系0 20 40 60 80 100320300280

27、260240220200s (MPa) (MPa/s)第35頁/共66頁2 2、Effects of temperature on mechanical properties of materialsGeneral tendency: As temperature increases, E、S andb descend ； and increase. As temperature decreases, b increases； and descend.)( C)MPa()GPa(E0 100 200 300 400 500216177137700600500400300200100100908

28、070605040302010(%),ESbEffects of temperature on mechanical properties of the low-carbon steel第36頁/共66頁二、溫度對材料力學性能的影響二、溫度對材料力學性能的影響總趨勢:溫度升高,E、S 、b下降； 、 增大。溫度下降,b增大； 、 減小。)( C)MPa()GPa(E0 100 200 300 400 500216177137700600500400300200100100908070605040302010(%),ESb溫度對低碳鋼力學性能的影響第37頁/共66頁200017501500125

29、01000 750 500 250 0-200 -100 0 100 200 300 400 500 600 700 800 )MPa()( Cb2 . 080706050403020100(%)Effects of temperature on mechanical properties of the chromium and manganese alloy第38頁/共66頁20001750150012501000 750 500 250 0-200 -100 0 100 200 300 400 500 600 700 800 )MPa()( Cb2 . 080706050403020100

30、(%)溫度對鉻錳合金力學性能的影響第39頁/共66頁As temperature decreases, the plasticity decreases and the strength limit increases. -0 5 10 15 302010 0C20C196C253 P(KN) Dl(mm)mid-carbon steel P(KN)-0 5 10 15 302010 0C20C196C253 Dl(mm)Pure iron第40頁/共66頁- P(kN)-0 5 10 15 302010 0C20C196C253 Dl(mm)-0 5 10 15 302010 0C20C19

31、6C253 P(kN) Dl(mm)溫度降低，塑性降低，強度極限提高純鐵中碳鋼 第41頁/共66頁As temperature decreases, b increases, why does the structure show the brittleness rupture at low-temperature?The Albert bridge of Belgium ruptured at low temperatures on March 4,1938.第42頁/共66頁溫度降低，溫度降低， b增大，為什么結構會發(fā)生低溫脆斷？增大，為什么結構會發(fā)生低溫脆斷？第43頁/共66頁The w

32、orking segment of the member can not go beyond the stable range tOABCDEUnstable rangeStable rangeAccelerative rangeDestroy range 0Creep curve of the material第44頁/共66頁構件的工作階段不能超過穩(wěn)定階段構件的工作階段不能超過穩(wěn)定階段 tOABCDE不穩(wěn)定階段穩(wěn)定階段加速階段破壞階段 0材料的蠕變曲線第45頁/共66頁Stress is not changed4321TTTTThe higher the temperature is, t

33、he faster the creep is.T1T2T3T41234Temperature is not changed1234The larger the stress is, the faster the creep is. 第46頁/共66頁應力不變4321TTTT溫度越高蠕變越快T1T2T3T41234溫度不變1234應力越高蠕變越快第47頁/共66頁3、Stress relaxation： At certain high temperature the general deformation of a member is not changed, while the elastic

34、 deformation will change into the plastic one with time, which results in the decreasing of stress in the member. This phenomenon is called stress relaxation. 第48頁/共66頁三、應力松弛：三、應力松弛： 在一定的高溫下，構件上的總變形量不變時，彈性變形會隨時間的增長而轉變?yōu)樗苄宰冃?，從而使構件內的應力變小。這種現象稱為應力松弛。第49頁/共66頁Temperature is not changed123213The larger th

35、e initial stress is, the larger the initial rate of relaxation is.Initial linear strain is not changed321TTTT1T3T2The higher the temperature is, the larger the initial rate of relaxation is.第50頁/共66頁溫度不變123213初應力越大，松弛的初速率越大初始彈性應變不變321TTTT1T3T2溫度越高，松弛的初速率越大第51頁/共66頁4、Mechanical properties of materials under the impact load impact ductility change temperatureWith the decreasing of temperature, b incr