【材料课件】第八章 强度理论.ppt
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1、,CHAPTER 8 STRENGTH THEORIES,1,材料力学,第八章 强度理论,2,CHAPTER 8 STHENGTH THEORIES,81 Concepts of strength theories 82 Four strength theories and their equivalent stresses 83 Mohrs strength theory and its equivalent stress,8-4 Applications of strength theories,3,第八章 强度理论,81 强度理论的概念 82 四个强度理论及其相当应力 83 莫尔强度理论
2、及其相当应力,8-4 强度理论的应用,4,1、Opening words:,8 CONCEPTS OF STRENGTH THEORIES,1)、Investigation of the tensile, compressive and torsional tests of cast iron and low-carbon steel,Cast iron,2)、How will the member rupture in Combined deformations?,STRENGTH THEORIES,5,一、引子:,8 强度理论的概念,强度理论,1、铸铁与低碳钢的拉、压、扭试验现象是怎样产生
3、的?,铸铁,2、组合变形杆将怎样破坏?,6,2、Theories of strength:Some assumptions about the cause of the strength failure of materials .,3、Types of failure of materials: yield; rupture,STRENGTH THEORIES,7,二、强度理论:是关于“构件发生强度失效(failure by lost strength)起因”的假说。,1、伽利略播下了第一强度理论的种子;,三、材料的破坏形式: 屈服; 断裂 。,2、马里奥特关于变形过大引起破坏的论述,是第二
4、强度理论的萌芽;,3、杜奎特(C.Duguet)提出了最大剪应力理论;,4、麦克斯威尔最早提出了最大畸变能理论(maximum distortion energy theory);这是后来人们在他的书信出版后才知道的。,强度理论,8,82 FOUR STRENGTH THEORIES AND THEIR EQUIVALENT STRESSES,1、Theory of the maximum tensile stress(the first strength): This theory considers the main cause of rupture to be the maximum t
5、ensile stress. The member will rupture as the maximum tensile stress reaches the strength limit in axial tension.,STRENGTH THEORIES,82 四个强度理论及其相当应力,一、最大拉应力(第一强度)理论: 认为构件的断裂是由最大拉应力引起的。当最大拉应力达到单向拉伸的强度极限时,构件就断了。,1、破坏判据:,2、强度准则:,3、实用范围:实用于破坏形式为脆断的构件。,强度理论,10,2、Theory of the maximum tensile strain(the se
6、cond strength): This theory considers the main cause of rupture to be the maximum tensile strain. The member will rupture as the maximum tensile strain reaches the limit strain in axial tension,STRENGTH THEORIES,11,二、最大伸长线应变(第二强度)理论: 认为构件的断裂是由最大伸长线应变引起的。当最大伸长线应变达到单向拉伸试验下的极限应变时,构件就断了。,1、破坏判据:,2、强度准则:
7、,3、实用范围:实用于破坏形式为脆断的构件。,强度理论,12,3、Theory of the maximum shearing stress(the third strength): This theory considers the main cause of rupture to be the maximum shearing stress. The member will rupture as the maximum shearing stress reaches the limit shearing stress in axial tension.,STRENGTH THEORIES,
8、三、最大剪应力(第三强度)理论: 认为构件的屈服是由最大剪应力引起的。当最大剪应力达到单向拉伸试验的极限剪应力时,构件就破坏了。,1、破坏判据:,3、实用范围:实用于破坏形式为屈服的构件。,2、强度准则:,强度理论,14,4、Theory of the maximum torsional (shearing)strain energy (the fourth strength): This theory consider the main cause of yield to be the distortional strain energy. . The member will rupture
9、 as the distortional strain energy reaches the distortional strain energy of yield in axial tension,STRENGTH THEORIES,15,四、形状改变比能(第四强度)理论: 认为构件的屈服是由形状改变比能引起的。当形状改变比能达到单向拉伸试验屈服时形状改变比能时,构件就破坏了。,1、破坏判据:,2、强度准则,3、实用范围:实用于破坏形式为屈服的构件。,强度理论,16,83 MOHRS STRENGTH THEORY AND ITS EQUIVALENT STRESS,Mohr thought
10、 the maximum shearing stress is the main cause of failure of materials ,but the friction force in the sliding section is not neglected. (Law of Mohr friction),Combining the factors of the maximum shearing stress and the maximum normal stress Mohr obtained his strength theory.,STRENGTH THEORIES,17,83
11、 莫尔强度理论及其相当应力,莫尔认为:最大剪应力是使物体破坏的主要因素,但滑移面上的摩擦力也不可忽略(莫尔摩擦定律)。综合最大剪应力及最大正应力的因素,莫尔得出了他自己的强度理论。,强度理论,18,Approximate envelope,Envelope of circles of limit stress,STRENGTH THEORIES,19,近似包络线,极限应力圆的包络线,O,t,s,一、两个概念:,1、极限应力圆:,2、极限曲线:极限应力圆的包络线(envelope)。,强度理论,20,1)、Criterion of failure:,2)、Strength condition:,
12、2、Mohrs strength theory:If the stress circle of an arbitrary point Contacts with the limit curve, the material will yield or break due to shearing .,STRENGTH THEORIES,21,2、强度准则:,1、破坏判据:,二、莫尔强度理论:任意一点的应力圆若与极限曲线相接触, 则材料即将屈服或剪断。,强度理论,22,3、Equivalent stress:(unified form of strength conditions),where, r
13、equivalent stress,3)、Application range:May be applied to the members with the failure form of plastic yield and the brittle members (rock、concrete and so on.)with different limit strength of tension and compression in complex stressed state.,STRENGTH THEORIES,23,三、相当应力:(强度准则的统一形式)。,其中, r相当应力。,强度理论,3
14、、实用范围:实用于破坏形式为屈服的构件及其拉压极限强度不等的处于复杂应力状态的脆性材料的破坏(岩石、混凝土等)。,24,84 APPLICATIONS OF STRENGTH THEORIES,1、Steps of calculation of strength:,STRENGTH THEORIES,25,84 强度理论的应用,一、强度计算的步骤:,1、外力分析:确定所需的外力值。,2、内力分析:画内力图,确定可能的危险面。,3、应力分析:画危面应力分布图,确定危险点并画出单元体, 求主应力。,4、强度分析:选择适当的强度理论,计算相当应力,然后进行 强度计算。,强度理论,26,2、Rules
15、 to select strength theories: decide according to the form of failure.,1)、Brittle materials:As the minimum principal stress is larger than or equal to zero the first theory may be applied; As the minimum principal stress is smaller than zero and the maximum principal stress is larger than zero Mohrs
16、 theory may be applied;As the maximum principal stress is smaller than or equal to zero the third or fourth theory may be applied;,2)、Ductile material:As the minimum principal stress is larger than or equal to zero the first theory may be applied;For the other stressed state the third or fourth theo
17、ry may be applied.,4)、Forms of failure are relative with temperature、speed of deformation etc.,STRENGTH THEORIES,27,二、强度理论的选用原则:依破坏形式而定。,1、脆性材料:当最小主应力大于等于零时,使用第一理论;,3、简单变形时:一律用与其对应的强度准则。如扭转,都用:,2、塑性材料:当最小主应力大于等于零时,使用第一理论;,4、破坏形式还与温度、变形速度等有关!,当最小主应力小于零而最大主应力大于零时,使用莫尔理论。,当最大主应力小于等于零时,使用第三或第四理论。,其它应力状态
18、时,使用第三或第四理论。,强度理论,28,Solution:Stressed state at the critical point A is shown in the figure:,Example 1 A circular rod made of cast iron is subjected to the loads T=7kNm, P=50kN as shown in the figure. Its diameter is d=0.1m, =40MPa. Try to check the strength of the rod according to the theory of the
19、 first strength.,Safe,STRENGTH THEORIES,29,解:危险点A的应力状态如图:,例1 直径为d=0.1m的圆杆受力如图,T=7kNm,P=50kN, 为铸铁构件,=40MPa,试用第一强度理论校核杆的强度。,故,安全。,强度理论,30,Solution:From generalized Hookes law we get:,This container does not satisfy the third strength theory and is not safe.,STRENGTH THEORIES,Example 2 As a circular th
20、in-walled tube is subjected to the maximum internal pressure, tested x=1.8810-4, y=7.3710-4. Knowing for steel E=210GPa,=170MPa, Possions ratio is =0.3. Check its strength according to the third strength theory.,31,例2 薄壁圆筒受最大内压时,测得x=1.8810-4, y=7.3710-4,已知钢的E=210GPa,=170MPa,泊松比=0.3,试用第三强度理论校核其强度。,解:
21、由广义虎克定律得:,所以,此容器不满足第三强度理论。不安全。,强度理论,32,Solution:Plot the diagram of Mohrtheory,STRENGTH THEORIES,Example 3 For a structural member made of cast iron, bL= 400MPa, by= 1200MPa. As a point with with the of plane stress yields according to Mohrs strength theory, the maximum shearing stress is 450MPa. Tr
22、y to determine the principal stresses at the point.,33,破坏判据:,例3 一铸铁构件 bL= 400MPa, by= 1200MPa,一平面应力状态点按莫尔强度理论屈服时,最大剪应力为450MPa,试求该点的主应力值。,解:做莫尔理论分析图,强度理论,34,STRENGTH THEORIES,That is,Criterion of failure:,35,强度理论,36,37,Chapter 8 Exercises 1. When establishing the strength conditions in the complex st
23、ress state, why can we determine the allowable stress of a material according to the results of the simple-tension test? 2. The first and the second strength theories are only suitable for brittle materials and the third and the fourth strength theories are only suitable for plastic materials. Can w
24、e say like this? Why? 3. Try to write out the expressions of the equivalent stress of a circular shaft in torsion according to the four strength theories. Solution:,STRENGTH THEORIES,38,第八章 练习题 一、在建立复杂应力状态下的强度条件时,为什么可以根据简单拉伸的试验结果来确定材料的许用应力? 二、第一和第二强度理论只适用于脆性材料;第三和第四强度理论只适用于塑性材料。这种说法是否正确,为什么? 三、试按四个强
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