Dynamics of Materials: Experiments, Models and Applications

599 Pages·2019·30.855 MB·English

by  Lili Wang, Liming Yang, Xinlong Dong, Xiquan Jiang

DYNAMICS OF
MATERIALS
Experiments, Models and
Applications
LILI WANG
LIMING YANG
XINLONG DONG
XIQUAN JIANG
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Preface for English Edition
Thanks to Elsevier and its editors, the English Edition of “Dynamics of
Materials” is about to go to press.
Unlike the cases under quasistatic loading, the mechanical response of
solids under dynamic (explosion/impact) loading is characterized mainly
by two dynamic effects, namely the inertial effects of structures and the
strain-rateeffectsofmaterials.Theinertialeffectofinfinitesimaldeformable
elementleadstothestudyofwavepropagationinvarious(preciseorsimpli-
fied)forms,promotingthedevelopmentofstresswavetheoryandstructural
impactdynamics,whilethestrain-rateeffectleadstothestudyofallkindsof
rate-dependent constitutive relations and failure criteria under high strain
rates, promoting the development of material dynamics. They are different
on the one hand and are interrelated on the other hand. It can be said that
the “Foundation of Stress Waves” printed by Elsevier in 2007 and the
“Dynamics of Materials” to be printed by Elsevier in 2019 are sister works
to each other.
The study of the dynamic mechanical response of materials can essen-
tially be attributed to how to quantitatively describe the whole process of
dynamic flow/deformation until final failure. The flow/deformation of
material is mathematically described by the constitutive relation, which
canusuallybedecomposedintoasphericalpartandadeviatorpart.Thefor-
merdescribesthelawofvolumetricchange(volumetriclaw),whilethelat-
ter describes the law of shape change (distortional law). Correspondingly,
this book consists of the following three aspects. In the first part, the
volumetriclawisdiscussedfromdifferentviews,includingitsmacrothermo-
dynamic basis, solid physics basis, and the related dynamic experimental
study. When the loading stress sL is much higher than the material shear
strength sS, the distortional part can be neglected, and the material can
then be approximately dealt with as a fluid. In such a case, the volumetric
law is usually referred to as the “Equation of State for Solids under High
Pressure.” In the second part, the distortional law is analyzed, wherein the
rate-dependentmacrodistortionallawdescribingstrain-rateeffect,itsmicro-
mechanism based on dislocation dynamics, and the dynamic experimental
research based on the stress wave theory are discussed in turn, one after
another. In the final part, the dynamic failure induced by dynamic damage
evolution is examined, including the unloading failure of crack-free body
j
vii
viii PrefaceforEnglishEdition
taking “spalling” as a typical representative, the crack dynamics for cracked
bodydescribingthecrackextensionofastationaryorpropagatingcrackun-
derdynamicloading,thedynamicfragmentationduetodynamicgrowthof
multicracks, and the dynamic evolution of meso-damage, first taking
Adiabatic Shearing as the representative and then the general evolution
law for different forms of meso-damage and macro-damage.
To help readers to understand the above contents more deeply and
extensively, this book tries to follow a comprehensive approach, i.e., the
approach characterized by the combination of macroscopic continuum
mechanics and thermodynamics, the combination of macromechanics
expressionandmicrophysicalmechanism,aswellasthecombinationofthe-
oretical analyses and experimental investigation.
LecturesonDynamicMechanicalPropertiesofMaterialsattheUniver-
sity of Science and Technology of China (USTC) could be dated back to
1962. In that year, Academician Zheng Zhemin advised me to teach the
course of Mechanical Properties of Metallic Materials Under Impact Load
to college students, who were the first students majoring in the Explosion
Mechanics Profession in the Department of Modern Mechanics. While
lecturing, I wrote corresponding lecture notes, which were reviewed and
approved by Academician Zheng and then printed for internal use (No.
07-58-b18). Different from traditional textbooks on the mechanical prop-
erties of metallic materials, this course is characterized by the combination
of mechanical properties of materials and the knowledge of stress waves. In
fact,theknowledgeofstresswaveshasbeentaughtsincethesecondchapter.
Two years later, it was changed to mainly focus on stress wave theory com-
bined with some corresponding contents of dynamic constitutive relation of
materials. A course on Plastic Dynamics was planned and corresponding
lecture notes were printed (No. 07-60-E08) for internal use in USTC.
In1978,IreturnedtotheUSTCfromnorthwestChina.Italsocoincides
withtheresumptionofthenationalgraduateenrollmentsystem.TheHead
oftheExplosionMechanicsProfession,Prof.ZhuZhaoxiang,attachedgreat
importance to the curriculum and teaching material of postgraduates. He
advisedmetoopentwointerrelatedcoursesforpostgraduatesoftheexplo-
sive mechanics profession, namely the Stress Wave Propagation and the
Material Dynamics courses. In addition to the graduates, he took the lead
andaskedyoungteacherstolistentothesetwonewcourses.Theheavybur-
den urges me to forge ahead. For me, lesson preparation is a process of
deeply consulting new literature and restudying. The lecture is a process
in which I give a presentation and then invite the audience to have
PrefaceforEnglishEdition ix
adiscussion.It’smorelikeaseminarthanalecture.Thatkindofatmosphere
withthetirelesscollectivelearningandlivelydiscussionforseekingthetruth
is by now unforgettable!
When the course of Stress Wave Propagation was retaught again at the
USTC, there were already old lecture notes, which, after being supple-
mented and edited, were published by National Defense Industry Press in
1985 under the title of “Foundations of Stress Waves.” However, when I
taught the new course of Material Dynamics, I only drew up a syllabus at
the beginning, as I did not have enough time to write the lecture notes.
Here I would like to thank my assistant, Lecturer Hu Shisheng. Using the
detailednoteswrittenbyhimwhenhewaslisteningtomylectureandrefer-
ring to the relevant materials, he sorted out the handout of “Material
Dynamics,”whichwasprintedmainlyforinternaluse.Until2013,thePress
of University of Science and Technology of China listed it as an Excellent
Textbook, and then it was coauthored by Wang Lili, Hu Shisheng, Yang
Liming, and Dong Xinlong and was officially published. During this time
Iwassuddenlyhospitalizedforsurgery,whichdelayedmyduedate.Iwould
like to take this opportunity to express my gratitude to my wife, Lu
Weixian, for her loving care, understanding, and support. I have not only
regained my health but also finished the revision work together with my
coauthors during my recovery. It lasted nearly 3years.
Whenwerevisedthismanuscript,althoughwestilldecidedtoemphasize
the basic principles, basic concepts, and basic knowledge, we also hoped to
reflect the new progress in this interdisciplinary field, as well as to reflect
some research results from Chinese scholars in this field.
The publication of this book also entailed the support of many col-
leagues.Amongthem,mycoauthorsandIwouldliketoexpressourpartic-
ular appreciation to Associate Professor Miao Fuxing, Dr. Ding Yuanyuan,
Dr.LeYang,andMr.ZhijinJonathanLin,whoassistedusinthetranslations
and the illustrations in this book.
Finally,Isincerelyhopethatthisbook,whichincorporatesmorethan40
yearsofteachingandresearchexperienceandtheinclusionofmanypeople’s
painstakingefforts,canpaveawayforthefutureyoungscholarsandensure
them a better future in climbing the new scientific peak!
Wang Lili (Lili Wang, Li-Lih Wang)
Professor, Key Laboratory of Impact and Safety Engineering
(Ningbo University), Ministry of Education
March 2019
CHAPTERONE
Introduction
Dynamics of Materials creates a new interdisciplinary branch, which studies
the basic law of high-velocity flow/deformation and dynamic failure of
materials under dynamic loading such as explosion and impact. It, together
withtheFoundationsofStressWaves,(Wang,2007)constitutestheimportant
foundation for studying Explosion Mechanics and Impact Dynamics. It is
also one of the important development directions in Material Science
research.
ForpeoplecomingintocontactwiththeDynamicsofMaterialsforthefirst
time,thedescriptionabove,aconcisedefinition,isnotclearenough.People
will raise a series of specific questions: What is the relationship between
material and mechanics? What is the relation between the Dynamics of
Materials and other classical courses such as Strength of Materials and Solid
Mechanics? What characteristics are expressed by the word “dynamics” in
the Dynamics of Materials?
Human beings live in the matter world. The views of “matter is
primary” and “matter is in motion” are the basic philosophical views for
understandingandtransformingtheworld.Inordertoknowandtransform
theworld,wemustfirstknowandstudythematterthatmakesupthematter
world. The matter to be studied and used is called material. Rock, for
example,isanaturalmatteraroundus,whenweuseitinconcretesasaggre-
gates, or as a target for ground-penetrating projectiles, it becomes rock
material when we study it.
Just as any science is closely related to matter, mechanics focuses on the
mechanical movement of matter. Therefore, the mechanical properties of
matter or materials play an irreplaceable important role in the study of
mechanics. As we all know, the basic equations of continuum mechanics
consistofthefollowingaspects:first,asetofgeometricequations(kinematic
equations) that relates displacements, strains, and particle velocities, etc.,
reflects the displacement continuity or the mass conservation in a
continuum. The second is the kinetic equation linking stress and particle
acceleration, which represents the momentum conservation. Another
set is the relation between various forms of energy, which embodies the
energy conservation. The last set deals with the relationship between
DynamicsofMaterials
ISBN:978-0-12-817321-3 ©2019ElsevierInc. j
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https://doi.org/10.1016/B978-0-12-817321-3.00001-2 Allrightsreserved.
2 DynamicsofMaterials
stress, strain and their time-derivatives, reflecting the intrinsic mechanical
properties of the material itself, called material constitutive relations,
and the corresponding mathematical expressions are referred to as the
materialconstitutiveequations.Amongthosebasicgoverningequations
incontinuummechanics,threeconservationequationsreflectthecommon
characteristics of each branch of mechanics, while the material constitutive
relationreflectsthespecialcharacteristicsofeachdifferentbranch.Review-
ing the formation and classification of the basic branches of continuum
mechanics, such as general mechanics (rigid body mechanics), fluid
mechanics, and solid mechanics, and so on, are they mainly distinguished
by the difference of constitutive relation of materials? It is no exaggeration
to say that the importance of constitutive relations in the development of
continuum mechanics cannot be overstressed.
In fact, the significance of the mechanical properties of materials is not
only that all mechanical analysis aimed at determining the mechanical field
(stress,strain,displacement,particlevelocitydistribution,etc.)ofanobjectis
based on the constitutive relation of materials, but is only half the task of
solving practical problem. More importantly to further answer whether
suchstresses,strains,displacements,andparticlevelocitiesexceedtheallow-
able limits so that will cause a failure of the object, it comes down to the
establishment of generalized strength criterion.
Any generalized strength criterion for quantitative analysis can be
reduced to the following simple
S (cid:2) Sc (1.1)
Once the formula is satisfied, it is judged either be of failure or invalid.
The S on the left side of inequality is a mechanical characteristic quantity
which can be computed from the basic governing equations mentioned
previously under given conditions, and is solved by mechanics scientists.
Forsolidstructures,thisisthetaskof“solidmechanics.”TheScontheright
side is a critical parameter that can be experimentally measured to charac-
terizethestrengthofmaterials,whichisreliedonmaterialscientiststosolve.
Inequality(1.1)linksthemechanicalcharacteristicquantitieswiththecritical
parameters of material strength. It means that strength analysis is simulta-
neously based on mechanics and material science, and there is no lack of
any one of them. If we do not have a comprehensive understanding of
the mechanical properties of materials, we cannot establish the above
strength criteria, and therefore cannot carry out any strength analyses.
Introduction 3
Both the study of the constitutive relation of various materials required
forthecalculationofSandthestudyofthestrengthparameterScofvarious
materials for the establishment of generalized strength criteria have formu-
lated a new discipline branch, the “Mechanics of Materials” in true sense,
which has nothing in common with the traditional university course
“Strength of Materials.” The latter, in fact, emphasizes the study not on
thestrengthofthematerialitself,butontheanalysisoftheforceanddefor-
mationoftypicalstructuralelements(suchasrods,shafts,beams,etc.)under
tension, compression, torsion, bending, and combined loads. The early
traditional course “Strength of Materials” did not distinguish between two
different concepts of mechanical response of structures and mechani-
cal response of materials. Scholars at that time did not distinguish
betweenstructuresandmaterials.Backtotheinequality(1.1),itisnotdiffi-
cult to understand that the S on the left side of the inequality involves the
structural mechanical response, while the Sc on the right side of the
inequality, as well as the constitutive relation required for the calculation
of the S, involves the material mechanical response.
Incidentally,inrelatedliteratures,besidesthetermmechanicalproper-
ties of materials, people will encounter other terms, such as the term of
mechanicalbehaviorofmaterialsandthetermofmechanicalresponse
of materials. They are related to each other but have different expressions
and meanings. Just as one’s inner thought determines one’s external
behavior, it can be understood as that the inner mechanical properties of
materials determine the external mechanical behavior of materials, while
the mechanical behavior of materials describes the mechanical response of
materials to various loads.
Studiesonthemechanicalpropertiesofmaterialsarebecomingmoreand
more important particularly because of all kinds of new engineering mate-
rialsareconstantlyemerging,theapplicationfieldofmaterialsisincreasingly
extensive, and the service conditions of materials have become more
extreme (high temperature, high pressure, high strain rate, strong magnetic
field, strong corrosion, intense radiation, and so on). The theme of this
book,namelythedynamicmechanicalpropertiesofmaterialsunderexplo-
sion/impact loading, is presently one of the most active directions in the
material mechanics field.
The term “dynamics” in the “dynamics of materials” is mainly to
emphasize the focus on the dynamic mechanical behavior of materials
under dynamic loading such as explosion and impact. Such intensive
4 DynamicsofMaterials
dynamic loads are characterized by a short duration, high amplitude, and
high variation rate over time. Therefore, unlike the problems under
quasi-static loading, for the problems under dynamic loading, as will be
discussed in this book as follows, the following characteristics should be
taken into account.
1.1 Short duration
Tocharacterizetheshortloadingdurationorprocesstimeofintensive
dynamic loading, let us introduce a characteristic time TL usually measured
intheorderofmicrosecondorevennanosecond.Ontheotherhand,intro-
duceacharacteristictimeTW¼Ls/Cwtocharacterizethedynamicresponse
ofthestructure,whereLsisthecharacteristiclengthofthestructureandCw
is the characteristic wave velocity of the stress wave propagating in the
structure. So the TW indicates the time a stress wave needs to travel across
a structural characteristic length. If the dimensionless time T is defined as
the ratio between TL and TW and is less than 1 (T ¼ TL/TW<1), namely
theloadingdurationisshorterthanthetimeittakesthestresswavetoprop-
agateacross thestructuralcharacteristiclength, thentheproblemcannotbe
treated as a quasi-static stress equilibrium problem, as the propagation of
stress wave in the structure must be considered. For example, if Ls is in
the order of a meter and Cw is in the order of 103m per second, then TW
is in the order of milliseconds. Thus if the characteristic time of an explo-
sion/impact load TL is in the order of microseconds or even 10(cid:3)1millisec-
onds, then the propagation of the stress wave must be taken into account.
1.2 Intensive loading
Forexplosion/impactloading,theloadingstresss ischaracterizedby
L
highamplitudeandawidevariationrange.Inordertoexpresshowhighthe
relativeamplitudeofanintensiveloadingis,introduceadimensionlessstress
s ¼s /s,wheres isthecharacteristicstresstodescribetheshearstrength
L s s
of materials. For example, in a nuclear explosion center, s can rise to the
L
orderof103e104GPawithinseveralmicroseconds,whiletheshearstrength
s of metals is generally in the order of 10(cid:3)1GPa, then the dimensionless
s
stress s is about in the order of 104e105. Obviously, under such intensive
loading,theshearstrengthofsolidmaterialscanberelativelyignored,likea
fluid.Thusthesolidmaterialcanbeapproximatelytreatedusingahydrody-
namic model. However, when s was decreased to the order of 101e100,