program plan

PROGRAM PLAN
ESIS-Workshop on
Numerical Modelling of Material's Failure
23./24. April 2009, University of Wuppertal, Germany
Program
Thursday, April 23, 2009
9:30 Registration
10:00 Opening
10:20 Session I: Numerical Methods (Chairman: Dr. Seifert)
10:20-11:00 M. Kübbeler, I. Roth, U. Krupp, C.-P. Fritzen and H.-J. Christ, Uni. of Siegen,
Germany
Simulation of stage I-crack growth using a hybrid boundary element technique
11:00-11:40 I.A. Khan, V. Bhasin, J. Chattopadhyay , K.K. Vaze, A.K. Ghosh, H.S.
Kushwaha; Bhabha Atomic Research Centre, Mumbai, India
Analytical modelling of crack-tip stress distribution in mismatch welded middle
crack tension M(T) specimen under plane-strain
11:40-12:20 J. Jackiewicz; University of Technology & Life Sciences, Bydgoszcz, Poland
Calibration of parameters for a micromechanical model of growth of microvoids
that may compete with shear in a polycrystalline metal by means of a genetic
algorithm
12:20-13:00 X. Pan, H. Yuan, Uni. of Wuppertal, Germany
Hyper-singular crack field analysis under gradient-dependent plasticity using
meshless methods
13:00-14:00 Lunch Break
14:00 Session II: Experimental Approaches (Chairman: Dr. Jackiewicz)
14:00-14:40 T Seifert, Ch Schweizer, M Schlesinger, M Möser, Fh-IWM, Freiburg,
Germany; M Eibl, BMW Germany
Thermomechanical fatigue life prediction of 1.4849 cast steel using a fracture
mechanics approach
14:40-15:20 Z. M. Shi, H. L. Ma, J. B. Li, Inner Mongolia University of Technology, Hohhot,
China
A new mesoparameter for describing plastic damage variation of microstructure of
ductile metal materials
15:20-16:00 U. Prahl, V. Uthaisangsuk, W. Bleck, RWTH Aachen, Germany
Damage and failure in multiphase high strength DP and TRIP steels
16:00-16:40 M. Madia, S. Beretta, Politecnico di Milano, Italy
Cyclic state of stress ahead of cracks and its implications under fatigue crack
growth
16:40-17:00 Coffee Break
17:00-18:00 Panel Discussions about ESIS TC8 (Chairman: Prof. Yuan)
19:00 Workshop Dinner in the Intercity Hotel Wuppertal (Main Station)
ESIS-TC8 Workshop on
Numerical Modelling of Material's Failure
23./24. April 2009, University of Wuppertal, Germany
Program
Friday, April 24, 2009
8:30 Session III: Modelling Methods (Chairman: Dr. Besson)
08:30-09:10 I. Scheider, W. Brocks, K.H. Schwalbe, GKSS, Germany
Recommendations for the application of the cohesive model based on various
studies
09:10-09:50 M.
Maziere, B. Fedelich, BAM Berlin, Germany
Opening displacement based cohesive zone models for fatigue crack growth
09:50-10:30 Y. Xu, J. Liu, H. Yuan, Uni. of Wuppertal, Germany
Damage evolution in cohesive models for characterizing low cycle fatigue cracks
10:30-10:50 Coffee Break
10:50-11:30 M. Vormwald, TU Darmstadt, Germany
Numerical simulation of plasticity induced fatigue crack opening and closure
11:30-12:10 S. Münstermann, F. Thönnessen, RWTH Aachen, Germany
Modelling the failure behaviour of ferritic steels in impact loading
12:10-12:50 D.W. Zhou. TWI Ltd, Granta Park, Cambridge, UK
R-curve and modelling and testing with constraint effect
12:50-14:00 Lunch Break
14:00 Session IV: Modelling Methods (Chairman: Prof. Vormwald)
14:00-14:40 J. Besson, Y. Shinohara, T. Morgeneyer, Y. Madi. Mines ParisTech CNRS,
France
Ductile rupture of prestained anisotropic metal sheets
14:40-15:20 M. Brünig, S. Gerke, D. Albrecht, TU Dortmund, Germany
Numerical analysis of inelastic behavior of ductile metals based on generalized
failure criteria
15:20-16:00 H. Krull, H. Yuan. Uni. of Wuppertal, Germany
Suggestions to cohesive traction-separation laws based on atomistic simulations
16:00-16:40 Ch. Zhang, X.W. Gao, Uni. of Siegen, Germany
3-D crack analysis in functionally graded materials
16:40-17:00 Closing Discussions and Remarks
Workshop Location:
Building B, Room 06.01
University Campus Grifflenberg
Wuppertal, Germany
Further information (www.nmmf.info):
Prof. Dr.-Ing. H. Yuan
Department of Mechanical Engineering
Bergische Universität Wuppertal, Germany
Phone: +49-202-439-2124 / 2018
Email: esis-tc8@uni-wuppertal.de
ABSTRACTS
Simulation of stage I-crack growth using a hybrid
boundary element technique
M. Kübbeler1 , I. Roth2 , U. Krupp3 , C.-P. Fritzen1 and H.-J. Christ2
1
Institut für Mechanik und Regelungstechnik - Mechatronik, Universität Siegen,
Deutschland
2
Institut für Werkstofftechnik, Universität Siegen, Deutschland
3
Fakultät Ingenieurwissenschaften und Informatik, Fachhochschule Osnabrück,
Deutschland
Email: kuebbeler@imr.mb.uni-siegen.de
Abstract
In many applications the service life of a component is controlled by propagation
of microstructurally short fatigue cracks. Stage I-crack growth occurs on single
slip bands and is influenced by the microstructure. Approaching a phase or grain
boundary, the crack propagation rate decreases and when overcoming the boundary
it increases significantly. This behaviour yields an oscillating crack growth rate and
cannot be quantified by concepts assuming material to be a continuum.
To simulate short crack propagation a two-dimensional model has been developed. Displacement discontinuity boundary elements are used to discretise the crack
allowing an opening and slide displacement of the crack flanks. Crack initiation and
accelerated crack growth can occur at loading conditions close to the fatigue limit
due to high local stresses in the vicinity of grain boundaries. They result from different elastic properties of the grains. To consider these properties in the model, each
grain needs to be enclosed, which is done by utilizing the direct boundary element
method to mesh the grain boundaries. A superposition procedure allows to employ
both boundary element methods in one model.
The problem of a crack in one grain can be divided into two sub-problems; the
crack in an infinite plate and the crack-free grain. The relative displacement of
the crack flanks causes a stress and absolute displacement field in the finite plate.
Deformation of the grain due to external loading produces stress inside the grain.
Superposition of the stresses and displacements from both methods along the crack
and the grain boundaries yields the solution of the total problem. This superposition procedure is carried out for each grain containing a crack. Subsequently the
grains are coupled along their common boundaries.
The simulation of stage I-crack propagation requires to consider the activated
slip band in front of a crack tip. For this purpose the slip band is discretised by
displacement discontinuity boundary elements, which can only carry out a slide displacement reproducing the elasticplastic behaviour of a slip band. The size of this
plastic zone is limited by the distance between the crack tip and the grain bound-
ary. In the neighbouring grain, stress increases while the crack is progressing to the
boundary. Shear stress along possible slip planes of this grain is evaluated. If a
critical stress intensity is exceeded on this plane, the slip band is activated and the
plastic zone extends into the adjacent grain.
The effect of different elastic properties in neighbouring grains is studied and
compared to a microstructure with grains of equal properties. It is found that the
critical stress intensity to activate the slip band in the adjacent grain is reached at
different crack lengths. Varying elastic properties also yields a change of crack tip
slide displacement controlling the crack progress.
Analytical Modelling of Crack-tip Stress
distribution in Mismatch Welded Middle Crack
tension M(T) Specimen under Plane-strain
I.A. Khan, V. Bhasin, J. Chattopadhyay , K.K. Vaze, A.K. Ghosh,
H.S. Kushwaha∗
Reactor Safety Division, Bhabha Atomic Research Centre, Mumbai-85, India
∗
Director, Health Safety and Environment Group, Bhabha Atomic Research
Centre, Mumbai-85, India
Email Addresses:imran@barc.gov.in; iak barc@yahoo.com
Abstract
Classical methods like Slip line field (SLF) analysis are applicable to macroscopically homogeneous/single material. Welded structures have a distinct interface on
which stress connections conditions are not known. Thus, SLF analysis can’t be
readily extended to analyse mismatch welds. In past, some investigators have made
an attempt to solve this problem analytically by assuming continuity of normal and
shear stress at the interface of base and weld material. However, this assumption is
not well supported by the results obtained from detailed elastic-plastic finite element
analysis. As a result, this approach could not become popular and many subsequent
investigations employed detailed FE analysis to obtain accurate results for this class
of problem.
Recently a modified Upper Bound approach (MUB) was proposed by Khan and
Ghosh [1] to overcome the limitations of classical Upper bound approach. It is well
known that the Upper bound approach of limit analysis is based on the assumption of
rigid blocks of deformation that moves between the lines of tangential displacement
discontinuity. This assumption leads to considerable simplification but often at the
cost of higher estimates of the actual load. Moreover, in many cases, it does not
give a correct shape of the plastic field. Although the proposed MUB method is
basically an energetic approach but unlike the classical upper bound approach it is
capable of including the presence of statically governed stress field and hence give
much better results. In subsequent work, Khan et al. [2] have established a rigorous
mathematical basis of this load bounding technique and it was demonstrated that
the proposed MUB method is actually a new form of the general extremum/work
principles. Minimization of this new form of work principle automatically satisfies
the global equilibrium equations. Thus, the equivalence of this new form of work
principle with the classical SLF analysis, for a homogeneous rigid-plastic material
in plane strain has already been established. In this work, a discontinuous stress
solution is proposed for mismatch welded M(T) specimen. Rigid-plastic material
model was assumed. Discontinuity is incorporated in the solution by assuming
an unknown value of normal stress at the interface of two materials. In addition
to global equilibrium equations, concepts of work principles have been utilized to
obtain this unknown normal stress and hence the whole plastic field near the crack
tip. The results obtained were found to be in excellent agreement with the known
FE solutions available in literature. In addition to limit load, detailed evaluation of
crack tip stresses have been worked out.
References
[1] A Modified Upper Bound Approach to limit analysis for plane strain deeply
cracked specimens, I.A. Khan and A.K. Ghosh, International Journal of Solids and
Structures, 44, 2007, 3114-3135.
[2] On the equivalence of slip-line fields and work principles for rigid-plastic body in
plane strain, I.A. Khan, V. Bhasin, J. Chattopadhyay and A.K. Ghosh, International
Journal of Solids and Structures, 45, 2008, 6416-6435.
Calibration Of Parameters For A
Micromechanical Model Of Growth Of Microvoids
That May Complete With Shear In A
Polycrystaline Metal By Means Of A Genetic
Algorithm
J. Jackiewicz
Department of Mechanical Engineering, University of Technology & Life Sciences,
Prof. Kaliskiego 7, PL 85-796 Bydgoszcz, Poland
Email Addresses:jacek.jackiewicz@mail.utp.edu.pl
Phone:+48-52-340-8252; fax: +48-52-340-8250
Abstract
Summary: Changes of stress or strain ratios during an operation can have an effect
on cracking during metalworking processes. Therefore, there is a substantive interest of the aluminum and steel industries of the manufacturing sectors in numerical
simulations of the fracture processes of typical structural materials. In the paper
a calibration procedure of material parameters for a combined fracture model of
the microvoid formation that competes with shear in the polycrystalline microstructure is described. The changes of void volume fraction or density may govern the
internal necking process at a location having a concentration of voids higher than
the average. Thus, the forming limit diagram can be predicted assuming that a
consequence of the coalescence of voids, which appears to be a local phenomenon
of structural instability leading quickly to the initiation of a crack, is the ductile
fracture process. Void coalescence in the material is not only determined by means
the so-called critical void volume fraction but also by the stress triaxiality factor.
The contribution then proceeds to evaluating the probability of structural failure
on the basis of the combined fracture model according to the calibrated material
parameters. An assessment of the probability of structural failure is important to
improve the quality of manufacturing processes, but also to reduce their costs.
Keywords: Micromechanical models for the simulation of ductile fracture, Kalman
filtering algorithm, Assessment of the joint probability density function, Searching
the extremum of the objective function with the evolution strategy.
Hyper-Singular Crack Field Analysis under
Gradient-Dependent Plasticity Using Meshless
Methods
Xiaofei Pan, Huang Yuan
Department of Mechanical Engineering, University of Wuppertal, Germany
Abstract
Singular stress field around a crack tip provides the fundamentals for fracture criteria. In strain gradient-dependent solids the stress singularity becomes non-uniform
as it in simple elastic-plastic materials. Based on the element-free Galerkin (EFG)
methods the singular stress and strain fields in strain gradient-dependent solids are
discussed in the present paper.
The paper starts with a brief overview of the strain gradient-dependent plasticity
models. The EFG method for finite strains is developed based on the gradient plasticity and implemented into the commercial code ABAQUS. Computations display
that the first-order strain gradient is necessary for the size effect in the plasticity,
while the second-order term of the plastic strain is used for delocalization against
strain softening.
The stress singularity shows substantial variations with the coefficients of the
plastic strain terms. Continuous variations of the strain gradients are studied numerically. Both evolution of the plastic zone and distribution of the stress/strain
around the crack tip show significant difference from the conventional results.
Thermomechanical fatigue life prediction of
1.4849 cast steel using a fracture mechanics
approach
Thomas Seifert∗ , Christoph Schweizer∗ , Michael Schlesinger∗ , Martin
Möser∗ , Martin Eibl∗∗
∗
Fraunhofer Institute for Mechanics of Materials IWM
∗∗
BMW Group
Email:thomas.seifert@iwm.fraunhofer.de
Abstract
High temperature components in combustion engines and exhaust systems must
withstand severe cyclic mechanical and thermal loads throughout their life cycle.
The combination of thermal transients with mechanical load cycles results in a
complex evolution of damage, leading to thermomechanical fatigue (TMF) of the
material and, after a certain number of loading cycles, to failure of the component.
Reliable computational methods are required allowing the calculation of the lifetime
and, thus, the optimization of the components via computer simulations.
In this paper a fracture mechanics approach is presented for the fatigue life prediction of 1.4849 cast steel used for exhaust manifolds and turbo chargers. Isothermal low cycle fatigue (LCF) tests and TMF tests are conducted in the temperature
range from room temperature up to 10000 C. A time and temperature dependent
cyclic plasticity model is employed to describe the transient stresses and strains.
The fatigue life prediction is based on a law for microcrack growth, which is the
predominant damage mechanism under the considered thermomechanical loading
conditions. The underlying idea of the crack growth law is that crack-tip blunting
in the tensile part of the cycle exposes fresh surface, which is quickly covered by
oxygen, so that rewelding of the crack faces is prevented during the compressive part
da
,
of the cycle. This irreversibility yields an increment in crack length in each cycle, dN
which is correlated with the cyclic crack-tip opening displacement, ∆CTOD. An analytical estimate of ∆CTOD is used, which is derived for non-isothermal loadings.
The fatigue lives of the LCF and the TMF tests are predicted well with the model.
Solely predictions for the LCF tests at 6000 C are non-conservative. Fractographic
investigations show, that fracture occurs intergranularly at 6000 C, while the fracture
surfaces show predominantly transgranular crack growth otherwise.
A new mesoparameter for describing plastic
damage variation of microstructure of ductile
metal materials
Z. M. Shi, H. L. Ma, J. B. Li
School of Materials Science and Engineering, Inner Mongolia University of
Technology, Hohhot, 010051, China
Email:shizm@imut.edu.cn
Abstract
The plastic deformation, damage and fracture of ductile metal materials are greatly
associated with the variation of microstructure of the materials. With an increase of
extra stress, there appear sequential stages of plastic deformation and ultimate fracture, which, in term of meso-dimension, correspond to the grain deformation caused
by dislocation movements and the nucleation, growth and coalescence of micro-holes
in local deformation. It is generally regarded that, the presence of micro-holes means
the on-set of damage of ductile metal materials. The micro-holes damage has been
paid great attention. However, it is very clear that before the micro-holes appear,
the microstructure has severely been changed, for instance, the grains are elongated
under the tensile loading. Therefore, how to seek the quantitative relationship between grain elongation and plastic deformation becomes a significant issue.
In the present work, we put forward
a new mesoparameter of relative shape
P
L
φ−φ0
P
factor of grains Φ(Φ = φ0 , φ = ( A ) Where L= The length of grain boundary,
A= The area of grains) to quantitatively describe the character of the microstructure, and a mesodamage parameter D(φ)(D(φ) = φφf )to describe the damage of the
microstructure during plastic deformation. With this concept, the quantitative relationship between microstructure and plastic deformation was constructed for Armco
iron and mild steel bars. The relationship perfectly discloses the variation of microstructure with plastic deformation and provides meso-criteria for the presence of
micro-holes.
Damage and failure in multiphase high strength
DP and TRIP steels
Ulrich Prahl, Vitoon Uthaisangsuk, Wolfgang Bleck
Department of Ferrous Metallurgy, RWTH Aachen University
Email:ulrich.prahl@iehk.rwth-aachen.de
Abstract
Multiphase high strength steels like DP and TRIP steel have been developed for the
automotive industry with regard to the purpose of the reduction of car body weight,
improved passive safety features, energy saving considerations, and environmental
protection. These steels show excellent strength and ductility due to the coexistence
of harder and softer phases in their microstructures. The damage mechanism and
failure behaviour of these steels is very complex and strongly affected by the microstructural components. In experiments, two failure modes were observed locally
in parallel on the micro-scale: cleavage and dimple fracturing. The void nucleation
is caused by the debonding of martensite from ferritic matrix. The carbon content
of martensite is also the important factor for the crack initiation. The relative contribution of each fracture mode is depending on the stress state (in particular the
triaxiality), the internal cleanness, the volume fraction of the retained austenite and
the locations of the neighbouring austenite grain and martensitic islands.
To describe the influences of the multiphase microstructures, an approach is presented using representative volume elements (RVE) within the framework of continuum mechanics. The microstructural characteristics as phase fraction, phase distribution or morphology, the phase interaction, and the different fracture mechanisms
of each individual phase are taken into account. Constitutive models describing the
mechanical properties of each phase were used concerning a carbon partitioning during intercritical annealing, chemical composition, and the dislocation theory. The
micromechanical Gurson-Tvergaard-Needleman (GTN) damage model was applied
for the RVE simulations to describe the ductile damage, occurring mostly in the
softer phase as ferrite. This damage model represents the fracture formation with
respect to the void evolution (void initiation, void growth and void coalescence).
Additionally, a phenomenological model, the cohesive zone model (CZM) based on
a separation law was used to represent a cracking mechanism as the debonding of
interfaces after reaching a critical deformation state. Real microstructures and determined phase fraction were considered for the RVE modelling. In this manner,
local stress strain distributions between different phases at the failure moment could
be studied, and correlated with the macroscopic formability. The resulted failure
prediction was verified with different experimental sheet forming testing.
The correlation between microstructure, local loading characteristic, mechanical
properties of the individual phases, and the failure behaviour will provide a better
understanding of the fracture mechanisms of the multiphase steels. Failure modelling
based on microstructure is a necessary tool for the steel and automotive industries to
design a precise microstructure and to optimise the properties of multiphase steels.
Cyclic state of stress ahead of cracks and its
implications under fatigue crack growth
M. Madia1 , S. Beretta1
Politecnico di Milano, Milan, Italy
Email:mauro.madia@polimi.it
Abstract
Numerical methods are mostly used in the field of fatigue to derive the stress intensity factor (SIF) or J-integral solutions to be employed in damage tolerance analysis
of cracked components [1]. In this frame, simple assumptions about material properties are taken into account.
More refined approaches [2,3] try to describe the plasticity induced crack closure
in order to account for retardation effects under variable amplitude loading. In these
approaches, the cyclic plasticity is used and cyclic finite element analyses are carried
out.
In the present work, a novel strategy [4] is presented for the calculation of the
relevant parameters to the fatigue-crack growth, based on the evaluation of local field
parameters (J-integral, T-stress) and cyclic material properties. It is demonstrated
that, in case of mild steels and under the assumption of a stress ratio R = -1, the
global constraint factor g, widely employed in fatigue-crack growth algorithms such
as the Strip Yield model [5], can be calculated in a closed form on the basis of the
expression of the crack-tip fields. Moreover, g provides a reasonable explanation of
the fatigue crack growth behaviour of the A1N steel for different geometrical and
loading configurations. Further investigations carried out on different medium and
high strength steel grades show that the plastic radius ahead of short and long cracks
at their fatigue limits can be considered as a constant for the material.
References
[1] M. Madia, S. Beretta and U. Zerbst. An investigation on the influence of rotary
bending and press fitting on SIF solutions and fatigue crack growth in railway axles.
Engng Fract Mech 2008;75:1906-1920.
[2] S. Pommier and Ph. Bompard. Bauschinger effect of alloys and plasticityinduced crack closure: a finite element analysis. Fatigue Fract Engng Mater Struct
2000;23:129-139.
[3] M. Sander and H.A. Richard. Finite element analysis of fatigue crack growth
with interspersed mode I and mixed mode overloads. Int J Fatigue 2005;27:905-913.
[4] M. Madia, Effect of constraint on crack propagation in mechanical components,
Ph.D. thesis, Milan, 2008.
[5] J.C. Newman Jr. A crack closure model for predicting fatigue crack growth
under aircraft spectrum loading. In: J.B. Chang, C.M. Hudson (Eds.), Methods
and models for predicting fatigue crack growth under random loading, ASTM STP
748, American Society for Testing and Materials 1981;53-84.
Recommendations for the application of the
cohesive model based on various studies
Ingo Scheider, W. Brocks, K.-H. Schwalbe
GKSS Research Center, Geesthacht, Germany
Email:ingo.scheider@gkss.de
Abstract
The cohesive model has been attracted so much attention in the scientific community
during the past decades that some general recommendation should be given in order
to enable engineers as well as scientists to apply the model without reinventing the
wheel every time. However, even in classical applications like crack propagation in
simple structures (simulation of residual strength and crack resistance curves) some
issues are still discussed controversially. For example: Has triaxiality dependence
to be taken into account? How can the parameters be identified? Has the tractionseparation law any effect on the results of the simulation or on the transferability?
and so on. Finally our achievements with respect to these issues will be shared and
a first draft of an application guide will be presented.
Opening displacement based cohesive zone models
for fatigue crack growth
M. Mazierea,b,∗ , B. Fedelicha
a
Bundesanstalt fur Materialforschung und-prufung (BAM), Unter den Eichen 87,
12205 Berlin
b
Ecole des Mines de Paris / CNRS, Centre des Materiaux / UMR 7633, BP 87,
91003 Evry, France
Email Addresses: Matthieu.Maziere@ensmp.fr
Abstract
Many numerical models are avalaible to simulate fatigue crack growth using finite
element method. Most damage models of the local approach to fracture combined
with classical elements lead to unexpected problem such as mesh dependency. To
avoid such problems, one can either use cohesive zone elements. These elements
based on the opening stress and displacement, originate from Dugdale model [1,2],
and have been later improved by [4]. Each element is in general governed by a
local damage variable that increase for each increment of loading, and remain equal
while unloading. This kind of approach is then denoted spatially and temporally
”
local” . A more realistic approach is proposed in this work introducing space and
time non-local variables.
Two different ” non local” model for cohesive zone elements are proposed in this
work. The first one is a full ” non local” model, where crack tip position denoted by
the global variable a is updated at each cycle beginning. The increment of a can be
governed either from J-integral [3], or in our case directly from the CTOD, i.e. from
the difference on a cycle between the maximum and the minimum of plastic opening
displacement at crack tip. Element are then separated in two group with suitable
material behaviors : safe ones ahead from crack tip, and broken one behind crack
tip. The second model is a time non-local model, but remain spatially local. A local
damage variable D is related to the local opening displacement, but updated just
once a cycle. The increment of D at a given integration point is directly governed by
the difference on a cycle between the maximum and the minimum of plastic opening
displacement at this integration point.
At this time, the full ” non local” model has been implemented in finite element
code Abaqus using a UMAT routine. This model has already been tested for many
load levels and ratio (∆ K and R), and will soon be compared with results provided
by the half non-local model.
References
[1] D.S. Dugdale. Yielding of steel sheets containing slits. Journal of Mechanics and
Physics of Solids, Vol. 8, 100104, 1960.
[2] B. Budiansky, J.W. Hutchinson. Analysis of closure in fatigue crack growth.
Transaction of the ASME, Vol. 45, 267275, 1978.
[3] K. Tanaka. The cyclic J-integral as a criterion for fatigue crack growth. International Journal of Fracture, Vol. 22, 91104, 1983.
[4] A. Needleman. A continuum model for void nucleation by inclusion debonding.
Journal of Applied Mechanics, Vol. 54, 525531, 1987.
Damage Evolution in Cohesive Models for
Characterizing Low Cycle Fatigue Cracks
Yangjian Xu, Jinxiang Liu, Huang Yuan
Department of Mechanical Engineering, University of Wuppertal, Germany
Abstract
Predicting fretting fatigue crack growth is a troublesome issue in computational
mechanics. The problem is related to both fatigue crack modeling under strong
mixed-mode loading conditions and robust numerical algorithm.
In the present paper an extended finite element method (XFEM) combined with
cyclic cohesive zone model (CCZM) is introduced for simulating fatigue crack propagation, which is implemented in the commercial general purpose software ABAQUS.
The algorithm allows introducing a new crack surface at arbitrary locations and directions in a finite element mesh, without needing to predefine the crack path and
remeshing as crack extension. For describing fretting cracking, a new cyclic cohesive
zone model has been introduced based on known S-N curves under uniaxial tests.
Computations confirm that the model approaches known fatigue features observed
in LCF tests.
To calculate the equivalent stress intensity factor for the cohesive fatigue crack,
the virtual crack closure technique has been extended to consider mixed-mode conditions. The crack propagation direction and rate under mixed-mode fatigue loading conditions are systematically studied using the boundary layer formulation and
verified by the known experimental data. Fretting fatigue crack initiation and propagation are predicted based on the XFEM computations. The results are validated
by and discussed with experimental data.
Finally the 3D crack propagation is modeled using the cohesive zone models.
The results show consistent development of the crack fronts under different loading
conditions. The crack growth rate, however, does not coincide with the known experimental observations which implies deficiency in the damage evolution equations.
Numerical simulation of plasticity induced fatigue
crack opening and closure
Michael Vormwald
Technische Universität Darmstadt
Email:breidenbach@wm.tu-darmstadt.de
Abstract
The mechanism of flank contact of a growing fatigue crack is of highest importance
in modelling the phenomenon. The origin of closure loads deviating from the expected value of zero has been attributed to plasticity, oxides, roughness, penetrating
media, or martensite transformation. Ignoring all of the latter causes the plasticity
induced crack closure remains to be a main mechanism providing a sound explanation for experimentally observed results of fatigue crack growth. Well known is
min
), meaning that the mean load of a cycle has
the so called R-ratio effect (R = FFmax
a high influence on the growth rates next to the applied load ranges. In addition
most but not all load sequence or load interaction effects can be nicely explained by
arguments stemming from plasticity induced crack closure (picc). Modelling of these
effects takes advantage from correlating the growth rate to the so called effective
range of the stress intensity factor, meaning the part of the cycle when the crack
flanks do not touch.
Early estimates of the crack opening load published soon after the discovery of
the phe-nomenon by Elber [1] used simple empirical formulas fitting experimental
results. Later Fhring and Seeger [2] as well as Newman [3] developed first mechanical models serving for both explanatory and prediction purposes. These models
are an extension of the Dugdale-Barenblatt [4,5] model allowing the fatigue crack
to grow in the plastically deformable strip. These models are part of actual fatigue
crack growth prediction software like for example NASGRO [6].
Ohji et al. [7] and again Newman [8] were the first to apply the nowadays mostly
applied numerical tool - the finite element method - to the problem of calculating
crack open-ing/closure loads and effective ranges. These early attempts have later
turned out to be cor-rupted by numerical deficiencies, see for example [9]. Up to
now discussion is continuing on the relevance of such analyses despite of their high
importance for an improvement of life prediction algorithms. This is due to a lack
of convergence and accuracy studies; see for ex-ample [10]. The necessary simplifications in the numerical analysis are the discrete propaga-tion equal to element size,
the propagation (change of boundary condition) at a specified load, a numerical
extremely high crack growth rate, sharp crack tips and weak plasticity models. The
list of influencing factors from numeric contains element size, debonding scheme,
mate-rial model, intermediate cycles and the observed flank region. Today there is
no accepted nu-merical procedure and there is nearly a complete lack of comparisons
between numerically determined measured picc. Therefore, a round robin might be
organized in ESIS TC 10 aim-ing at a comparison of numerical results obtained by
various individual procedures, figuring out the reasons for differences and improving
numerical skills of the participants by compar-ing with experimental results supplied
by a high-skilled lab. Topics to investigate might in-corporate the list of influence
factors from numeric, the R-ratio effect, 2D and 3D structures, variable amplitudes,
remeshing enforced by curved crack paths, environmental effects when comparing
with experimental results and extending the analysis to include micro-structural
aspects.
References
[1] Elber W. Fatigue crack closure under cyclic tension. Engng Fract Mech 1970;2:3745.
[2] H. Führing, T. Seeger. Dugdale Crack Closure Analysis of Fatigue Cracks under
Constant Amplitude Loading. Engng Fract Mech 1979; 11: 99-122.
[3] J.C. Newman, Jr. A crack-closure model for predicting fatigue crack growth
under aircraft spectrum loading. ASTM STP 748, 1981, 53-84.
[4] D.S. Dugdale Yielding of Steel Sheets Containing Slits. J Mech Phys Solids.
1960;8:100-104.
[5] G.I. Barenblatt. The formation of equilibrium cracks during brittle fracture.
PMM 1959;3:434-444.
[6] www.nasgro.swri.org
[7] Ohji K, Ogura K, Ohkubo Y. On the closure of fatigue cracks under cyclic tensile
loading. Int J Fract 1974;10:123-4.
[8] Newman Jr J. Finite element analysis of fatigue crack closure. ASTM STP 590
1976. 281-301.
[9] Sehitoglu H, Gall K, Garcia A. Recent advances in fatigue crack growth modeling. Int J Fract 1996;80:165-92.
[10] E. Herz, R. Thumser, J.W. Bergmann, M. Vormwald. Endurance limit of autofrettaged Diesel-engine injection tubes with defects. Enging Frac Mech 2006;73:321.
Modelling the failure behaviour of ferritic steels
in impact loading
S. Münstermann, F. Thönnessen
Department of Ferrous Technology, RWTH Aachen University
Email:sebastian.muenstermann@iehk.rwth-aachen.de
Abstract
For the assessment of structural integrity, mainly strength and toughness properties
of the selected material are evaluated. Especially for components in severe loading
conditions (e.g. pipelines made of HSLA steels), highest toughness requirements are
defined. In order to be able to produce high strength steels with excellent toughness properties, a quantitative understanding of the influence of microstructure on
toughness properties is required. For ductile failure behaviour, micromechanical
damage models offer the possibility to correlate parameters of the void evolution
law to results of quantitative metallographic investigations.
Many HSLA steels exhibit excellent strength and toughness properties which
are a result of precisely adjusted quenched and tempered microstructures and good
cleanliness. Their ductile failure behaviour is on the one hand controlled by nucleation and growth of primary voids nucleating at those few non-metallic inclusions
that can still be found in the materials microstructure. On the other hand, nucleation and growth of a second void population with significantly smaller size plays an
important role for the ductile failure process in these steels. As the void evolution
law of the ductile damage model by Gurson, Tvergaard and Needleman considers two
void populations, it seems to be adequate to model the ductile failure behaviour of
such steels with good cleanliness. Hence, the presentation will focus on a methodology to quantify the model parameters of the void evolution law based on the results
of metallographic investigations. Especially the parameters describing nucleation
and growth of secondary voids will be emphasized. The second part of the simulation will focus on simulation of Charpy tests using the parameter sets resulting
from metallographic investigations. Finally, the results are discussed critically and
an outlook to future activities will be given.
R-Curve and Modelling and Testing with
Constraint Effect
D.W. Zhou
TWI Ltd, Granta Park, Great Abington, Cambridge, UK, CB21 6AL
Email: daowu.zhou@twi.co.uk
Abstract
The structural integrity of components is usually carried out using the specimen
fracture resistance curve (R-curve). However, the specimen R-curve significantly
differs from the component fracture resistance due to the presence of constraint
at the crack tip. Current R-curve measurement methods are for high-constraint
specimens only and this is over-conservative when the flawed structure is under low
constraint level.
Methods for R-curve testing of low constraint strength mis-matched welded joints
were investigated. Three distinct measurement methods were used for R-curve testing, ie, the single specimen unloading compliance method, single specimen normalization method and multi-specimen method. The specimens investigated included
single edge notched bending (SENB), single edge notched tension (SENT) and center cracked tension (CCT) specimens with various crack lengths.
The measured results were used for R-curve modelling and validation. Three
constraint effect theories (T stress, Q stress and J-A2 theory) were used to construct
the constraint-based R-curves. The predicted R-curves were compared against the
tested results. Conclusions on the feasibility of the constraint parameters for Rcurve modelling were drawn. The developed theories can be potentially used for
engineering critical analysis (ECA) in various industry sectors.
Ductile rupture of prestained anisotropic metal
sheets
Jacques Besson, Yasuhiro Shinohara, Thilo Morgeneyer, Yazid Madi
Centre des Materiaux, Mines ParisTech CNRS UMR 7633
Email: jacques.besson@ensmp.fr
Abstract
Metals sheets are used in numerous industrial applications which require safety assessment. This include aluminum alloy sheets used in the aerospace industry, steel
sheets used to produce line pipes, zirconium alloys used to manufacture nuclear fuel
assemblies. . .Compared to thick structures such as pressure vessels, which have
been studied for many years, thin walled structures present some specific rupture
properties which needs to be characterized:
1) Sheet metal often exhibit a strong plastic anisotropy both in terms of yield
stress and Lankford coefficient due to texture development during processing. Such
plastic behavior may influence local stress levels in structures and consequently the
onset of ductile rupture.
2) Processing may also lead to anisotropic defect distributions and to subsequent
rupture anisotropy.
3) Due to the small wall thickness, stress triaxiality, which controls ductile damage growth kinetics, is reduced compared to thicker structures so that failure mechanisms may differ from the usual failure process by nucleation, growth and coalescence
by internal necking.
4) Metal sheets are often prestrained before use (see e.g. aluminum sheets used
to manufacture aircraft fuselage or steel plates used to produce pipeline elements).
Prestrain both hardens and damages materials so that fracture properties (e.g. ductility and toughness) of the final product may differ from those of the unstrained
materia.
The presentation will illustrate these different points and present ways to account
for them in a model derived from the GursonTvergaardNeedleman model for ductile
fracture. Emphasis will be put on modelling of plastic and rupture anisotropy and
prestrain effects which require the use of kinematic hardening.
Numerical analysis of inelastic behavior of ductile
metals based on generalized failure criteria
Michael Brünig, Steffen Gerke, Daniel Albrecht
TU Dortmund University, Dortmund, Germany
E-mail: michael.bruenig@tu-dortmund.de
Abstract
The presentation deals with numerical simulation of the inelastic behavior of aluminum alloys based on generalized damage and failure criteria taking into account
various triaxial states of stresses.
The accurate and realistic modeling of inelastic deformations as well as of damage and failure behavior of ductile materials and structures under general loading
conditions is essential for the numerical solution of numerous boundary-value problems occurring in various engineering disciplines. Within the general framework of
continuum thermodynamics of irreversible processes a thermodynamically consistent anisotropic damage and failure model based on kinematic definition of damage
tensors is discussed. The continuum model is based on free energy functions defined
in fictitious undamaged and damaged configurations, respectively, leading to elastic
material laws which are affected by damage. It is now well known that besides stress
intensity, stress triaxiality is the most important factor that controls initiation of
plastic flow, damage and fracture. In this context, a generalized hydrostatic-stressdependent yield condition and a non-associated flow rule are used to adequately
describe the plastic behavior of ductile metals. Furthermore, a damage criterion
formulated in stress space is proposed based on a series of experiments with various notched tension and shear specimens manufactured from aluminum alloy sheets
used in aircraft industry. In addition, a failure criterion based on critical damage
parameters is discussed. Different branches of the damage and failure criteria are
taken into account corresponding to different damage modes depending on stress
triaxiality and Lode parameter.
Corresponding numerical algorithms are discussed in detail and the applicability
of the continuum model is demonstrated by numerical simulations. In this context,
identification of material parameters is presented. The new damage-failure approach
allows realistic numerical simulation of the shear and tension tests up to final fracture
and elucidates different mechanisms on the micro- and macro-scale.
Suggestions to the Cohesive Traction-Separation
Law Based on Atomistic Simulations
Heiko Krull, Huang Yuan
Department of Mechanical Engineering, University of Wuppertal, Germany
Abstract
To investigate the failure of ductile materials the cohesive zone model gives feasible
results, which could provide a more detailed understanding of the failure mechanism.
In the cohesive model, however, the major difficulty is to formulate a reasonable
cohesive traction-separation law, especially for mixed-mode loading conditions.
In the present paper suggestions of the cohesive law based on constrained threedimensional atomistic simulations are presented. A classical molecular dynamics
code is used to study the growth of a nanoscale crack in single-crystal Aluminium
based on the EAM potential. The main focus of the work is on carry out relations
between the local stress distribution and material failure under mode I loading
condition. To examine effects of loading configurations, some mode II loading cases
are considered.
In the mode I loading case it is found that crack growth is in the form of void
nucleation, which is similar to ductile fracture at the continuum scale. A concentration of the atomistic mean stress at a certain distance ahead of the crack tip, where
also the void nucleation occurs, is observed. It implies that the material failure
under mode I is dominated by the normal traction. The atomistic stresses are used
to provide theoretical background for cohesive zone model and and to identify the
cohesive traction-separation law.
3D crack analysis in functionally graded materials
Ch. Zhang1 and X. W. Gao2
1
Department of Civil Engineering, University of Siegen, D-57068 Siegen, Germany
Email: c.zhang@uni-siegen.de
2
School of Aeronautics and Astronautics, Dalian University of Technology,
Dalian,116024, PR China
Email: xwgao@dlut.edu.cn
Abstract
Functionally graded materials (FGMs) represent a new class of advanced composite
materials with continuously nonhomogeneous material properties. In recent years,
FGMs received considerable attention in material sciences and engineering applications, because FGMs benefit from the ideal performance of their constituents,
e.g., high heat, corrosion and wear resistances of ceramics on one side, and large
mechanical strength, toughness and good workability of metals on the other side.
In practical situations, cracks or crack-like defects are unavoidable in FGMs, which
may be induced by materials processing and in-service loading conditions. For this
reason, fracture and fatigue analyses of FGMs are of considerable interest for their
reliability and durability in engineering applications. Due to the complexity of the
problem, fracture and fatigue analyses of FGMs demand efficient and sophisticated
numerical methods such as the finite element method (FEM), the boundary element method (BEM), and the recently developed meshfree or meshless methods.
Most of the previous investigations on crack analysis in FGMs were devoted to twodimensional (2D) problems, and only few works for three-dimensional (3D) problems
are yet known in literature.
In this paper, recent advances on 3D crack analysis in FGMs are reported and
discussed. In particular, a BEM for solving crack problems in 3D, isotropic, continuously non-homogeneous and linear elastic FGMs is presented. The present BEM
is based on a boundary-domain integral equation formulation, which applies the
fundamental solutions for 3D, isotropic, homogeneous and linear elastic solids. The
material non-homogeneity is considered in the formulation by a domain-integral. To
avoid the displacement gradients in the domain-integral, normalized displacements
are introduced in the present boundary-domain integral equation formulation. The
present BEM is a meshfree or meshless method, since no internal cells or meshes are
needed for computing domain-integrals in the boundary-domain integral equations.
An efficient numerical solution technique based on a three-step solution strategy and
a multi-domain BEM is implemented to reduce the computational effort, which is a
critical issue for 3D crack analysis. To show the effects of the material gradients on
the stress intensity factors, numerical examples will be presented and discussed.