Rheology, Physical and Mechanical Behavior of Materials, Volume 5

Maurice Leroy is a doctor in physics and solid mechanics, and a lecturer and professor at the University of Nantes, France, as well as Director of the Composite and Metallic Formations research laboratory at the IUT. He was instrumental in the creation of France’s first Materials Science and Engineering department.

• Chapter 1 Damage 11.1 Definition 11.2 Damage variables 21.3 Effective stress 31.4 Principle of strain equivalence 51.5 Experimental characterization of the damage 61.5.1 Changes in mechanical characteristics 61.5.2 Modifications of the material 71.5.3 Wear rate 71.6 Models of the progression of the damage D 91.6.1 Dissipation 91.6.2 Types of damage 10Chapter 2 Ductile Fracture 172.1 Stages of ductile tearing 172.1.1 First step: damage by decohesion, cracking of inclusions, impurities, precipitates, cavity formation 172.1.2 Second stage: growing cavities, formation of peduncles followed by necking, giving rise to ductile tearing 182.2 Linear ductile plastic damage during strain 202.3 Formation of cracks around inclusions or precipitates, cavities in ductile fracture 232.3.1 Formation of cracks from particles for Figure 2.5(b): the case of multiple metals 282.3.2 Aluminum–silicon alloy 292.4 Analysis of facies of ductile fractures of trichite and metals according to the purity and the state of the stresses 302.4.1 Whisker fracture (Cu and Fe) 302.4.2 Polycrystals CC and CFC in ductile fracture: influence of stress states and purity 332.4.3 Ductile fracture of steel test pieces without notches 342.4.4 Fracture of pure iron specimens 352.4.5 Ductile fracture of industrial copper specimens of purity 4N and 5N 362.4.6 Cases of zones of melted Fe, Cu (4N, 5N and industrial), aluminum (3N, 5N and industrial) – uniaxial and triaxial stresses 402.5 Relationship between the density of inclusions and ductility 442.5.1 Sintered copper made up of particles 442.5.2 Alumina 46Chapter 3 Sudden Fracture, Fracture Energy 533.1 Analysis of the fracture 533.2 Sudden fracture and energy criterion 543.2.1 Energy balance causing the crack to advance 543.2.2 Obtaining Gc 563.2.3 Data for Gc and Kc 583.2.4 Examples of sudden fractures 64Chapter 4 Description and Modeling of Physical Mechanisms 734.1 Expansion of cracks 734.2 Calculation of rp : the case of confined plasticity 744.3 Elastoplastic zone at the end of a crack 764.4 Stress and strain field at the end of the crack 77Chapter 5 Fractures due to Cleavages and Intergranularity 815.1 Fractures from cleavages 815.1.1 Examples of fractures by cleavage 825.1.2 Change of micromechanisms 845.2 Intergranular fracture 855.2.1 Fractures along interfaces, grain boundary 855.2.2 Intergranular brittle fracture 865.2.3 Metal fracture transition parameter 875.2.4 Influence of the grain boundary 915.2.5 Cleavage strain of steels 925.2.6 Influence of the addition elements on the brittle–ductile transition 93Chapter 6 Concentration of Stresses K t 976.1 Introduction 976.2 Measure of Kt 996.2.1 By extensometry gauges 996.2.2 By photoelasticimetry 1006.3 Solids with equal resistances 1016.4 Notching effect 1026.5 Reduction of the stress concentration factor: the case of notched objects 1046.6 Effect of notches under fatigue 1056.7 Stress concentration values Kt : useful cases in practice 107Chapter 7 The Intensity Factor of Stresses K 1117.1 Introduction 1117.2 Fields of stresses and movements 1137.2.1 Mode I 1137.2.2 Mode II 1157.2.3 Mode III 1177.2.4 Values of K for flat cracked medium 1187.2.5 Area at the bottom of the crack 1217.2.6 Influence of the plastic zone undergoing cracking 1247.3 Remarks regarding K = σ √πa 1257.4 Values of the stress intensities KI , KII , KIII for the three modes: for cases related to the subject and useful cases in practice 1267.4.1 Typical values of stress intensity factors KI , KII , KIII 1267.4.2 Values of K I = f(λ).σ√πa 131Chapter 8 Fracture Zones in Photoelasticimetry 1378.1 Photoelasticity 1378.1.1 Primary stresses and isostatic lines 1378.1.2 Birefringence by strain 1388.2 Propagation of light vibrations 1398.2.1 Propagation of light in a vacuum 1398.2.2 Propagation of light in a transparent medium 1408.2.3 Wave in a dielectric 1418.2.4 Values of the constants C and K of photoelastic materials 1428.2.5 Choice of a photoelastic coating 1448.2.6 Ellipsoid of the indices 1468.3 Photoelasticimetry 1498.3.1 Photoelasticimeter 1498.3.2 Isochromatic lines, difference between the primary stresses 1518.3.3 Example of physical parts under stresses: a three-dimensional case using the freezing method 159Chapter 9 The Influence of Strain Speeds 1619.1 Types of dynamic loads 1619.2 Examples of fast fractures 1639.3 Damage, domain between necking and fracture, the case between FLCS and LCFF 1689.3.1 Definition 1689.3.2 Large strains and damage 1699.4 Forming limit curves: static stamping (under a press) and dynamic stamping (magnetoforming and electrohydroforming) 1719.4.1 Measurement of strains 1719.4.2 Description of an electrohydraulic (EH) test 1729.4.3 Types of test pieces 1769.4.4 Example of LCFFs 1779.5 Shock by intense pulsed magnetic field on aluminum alloys 1809.6 Test results 1839.6.1 Strain trajectories, change of ε 1 according to ε 2 ; comparison of low and high speeds 1849.6.2 Influence of strain speeds on FLCs, formability in static and dynamic states 1879.6.3 Comparison of the values for necking Z and fracture F 189Chapter 10 Metal Fatigue 19710.1 Introduction 19710.2 Endurance curve: plot of the endurance curve or Wöhler curve 19710.3 Conventional endurance limit 19910.4 Classification of fatigue tests 20110.4.1 Definition 20110.4.2 Tests in practice 20310.4.3 Combined stress tests 20510.4.4 Application of a criterion in planar stress 21210.4.5 Examples of influences on endurance 21610.4.6 Influence of temperature 21710.5 Physical aspects of fatigue 21910.5.1 Physical mechanisms 21910.5.2 Fatigue fracture surfaces, microscope images 22210.5.3 Change of the streak spacing 22310.5.4 Examples of micrograph images of fractures 22410.6 Types of fatigue 22510.6.1 Behavior of non-cracked parts under fatigue 22610.6.2 Behavior of non-cracked parts under fatigue 23010.7 Plasticity, fast fracture by fatigue: a case study 23510.8 Propagation of corrosion cracks under fatigue-corrosion stress and influence of cycle frequencies 241Chapter 11 Fracture of Composites 24711.1 Fracture mechanisms 24711.1.1 Unidirectional composite (UD) 24711.1.2 Fracture of laminates 25211.2 Criteria for fracture 25411.2.1 Data describing the resistance of a UD or a fabric 25411.2.2 Successive fractures of layers 25611.2.3 Strength/stress ratio: coefficient of resistance R 25611.2.4 Criteria for maximum stress and/or maximum strain 25711.2.5 Quadratic criterion: in the stress space 25911.2.6 Fracture envelopes 26411.3 Design in primary strains 26611.3.1 Principal stresses and strains 26611.3.2 Constants of stresses and strains 26711.3.3 Scaling of isotropes 268Appendices 275References 331Index 335