t) EDP Sciences, Les Ulis

DOI : 10. 1051/jp4 : 20030716

Experimental and numerical modeling of the heterogeneous

materials fracture

V. V. Lepov, E. A. Arkhangelskaya, V. T. A) ymov and V. P. Larionov

IPTPN SB RAS, 1 Ul. Oktyabrskaya, 677891 Yakutsk, Russia

IMASH RAS, 4 Ma/uy Kharitonievskií Pero, 101990 Moscow, Russia

Abstract : The complex evolution and hierarchical approach to the modeling of the heterogeneous viscous-plasticdamaging media fracture process is considered. The developed for the stochastic crack growth in the defects arraymodel allowed visualizing the process of crack propagation on the base of microdefects nucleation mechanism,the small cracks growth and coalescence under the extemal stress and hydrogen effect. Macroscopie model basedon the deterministic approach and could simulate the damage accumulation and fracture process of metal duringthe hydrogen induced delayed fracture. Experimentally by the optical, electronic probe fractography and scanningtunneling " in situ " microscopy methods the statistical parameters and its evolution during the deformation of theheterogeneous material bas obtained. The possibility of model use for the modeling ofaluminum alloy hot tearingduring the solidification process bas shown. The evolution of the damage up to ultimate material state modeling inthe scale of the part has shown.

1. INTRODUCTION

As the number of authors have shown [1, 2], there is no theory today that could explain the strength anddeformation properties of solids without the empiric approach use. Meanwhile, nevertheless of someanalogous use attempts [3], the construction of such the theory of solids is impossible in the frames ofclassical physics [1]. In common case the quantum-mechanical representations that based on the exactstatistical description of the real structure of heterogeneous defect material it is necessary to implicate.

Such the statistical approach, based on the development of defect field theory in relativistic continuum in

common case, and supplemented by the experiment physical data on different structural levels o f realmaterial, is peculiar to stochastic structural models of solids. One of the possible realization of such

model is the stochastic model of microdefects opening, growth and mutual coalescence of small cracks,

and propagation of a main crack in a multiphase, heterogeneous material. The attraction of theory of

dispersed damage accumulation that describes the strength loss under the different damaging influences

(force, fatigue, corrosion, radiation, thermal etc.) is necessary in more common case. The peculiarity if

such a model is a capability of joining of the process that occurred on the different structural levels

simultaneously [4].

The stress induced opening of a defect, which growth and coalescence take place on the mesolevel, in

such a model corresponds the ultimate state achieved on the previous structural level, and could be

estimated by some measure of the local damage. Further cooperative growth of the mesodefects in the

form of micropores and micro cracks with different orientation is occurred in accordance with the defined

material model. The defects coalescence with each other and main crack is the process that runs on the

mesolevel also.

The real properties and quantitative attributes (size, concentration, shape) of inclusions in the material (as

well as in the polymer structure and in the grain boundaries of polycrystalline) has been obtained by the

optical and electronic tunnelling microscopy directly, and on the base of optical-video image recognition

and X-ray diffraction methods of the surface of deformable " in situ " and already fracture specimens [5,

6, 7].A structural approach of the activation effect of active media (like hydrogen etc.) on the structure of

processes of the material deformation and fracture on the basis of theoretical and experimental research

was offered. It takes into account the hierarchical material structure. On the basis of such approach the

known experimental effects of changing of the mechanical characteristics during the delayed fracture of

steels under the influence of hydrogen and extemal loading at low climatic temperatures was explained.

It was clarifie also that the most probable mechanism of the delayed fracture of steel under the influenceof hydrogen is the formation of a special hierarchical structure of deformation that stipulates a structuredlocalization tum at the macro level because of an increasing mobility of dislocations on the micro level.Realisation of this mechanism is possible only by a discontinuous advance of a micro crack accounted forthe diffusion-dislocation processes until it reaches the critical length, stipulated by the mesostructuralstructure, after that a microcrack leaps to the undamaged area. the series of experimental and theoreticalinvestigations are shown that just the dislocation transport provide the increase of local hydrogen contentin the intensive strain area of material when the density of material structure defects are sharply rise. Atthe same time the hydrogen is accumulated in defects-the traps in metal [8, 9] that decrease the metalresistance against the hydrogen embrittlement.It should be noted that nevertheless of the huge experimental data presence the theoretical basis that givesthe chance to investigate a physical nature of cold brittleness on the level of collective electrons,interatomic force values, type of atomic bonding, distortion and changing of the crystal lattice type,particularly for the new construction alloys design, at modem stage of material science development, thefull model of the deformation and fracture is absent. On the one hand, the mechanical and materialengineers operate only by the phenomenological theories that are not connecte with the actual materialevolution and until now. On the other hand, the big knowledge potential about the internal structure ofmatter in the solid state physics has accumulated, and it remains unclaimed by material engineers.The conceptual scheme of the modelling of processes of deformation and fracture of heterogeneousmaterials on the basis of evolution and hierarchical approachs is shown on Fig. 1. It demonstrates thesignificance of the connection as well as the continuum and statistical approaches, and micro-, meso-andmacro-modeling descriptions. The evolution approach in last years are significant due to it possibility totaking into account the material and structure history.

AsseMbly of mater'al physioal,. !. I I I I _. I.

force, tomperature, coroslon loadlnoparameters

on esàl'ov'l'

The estîmation of structure ultimate etate and lifetimetakinq into account the reai evolution of properties

and defect structure of materîal

Fig. t. Conceptual scheme of the modeling of the heterogeneous media deformation and fracture processesbased on the evolution and hierarchical approaches.

2. DEFECT STRUCTURE STUDY

To reveal the mechanism of metal fracture under low temperatures, the fracture surfaces of constructionelements and sample models are being studied. Optical and tunnelling scanning fractography of fracturesof samples, fractured under different extemal environments and after different types of influences on themetal is being realised, a complex of metallographic and microstructure studies was carried out.So the model small-size specimens that were saturated at high temperature and high pressure byhydrogen, and the welding thermocycling samples, and a part of self-fractured at stress corrosionconditions wheel rim of heavy hauler was investigated. It is necessary to define the microdefects(inclusions, microcracks, micropores) size distribution function, its shapes and average concentrationdepend upon the static and corrosion influence, for the obtaining the probabilistic estimation.Using the method oftunnelling electron microscopy a fracture ofsteel 14H2GMR samples was explore.The samples were saturated preliminarily by the hydrogen in the 400C temperature and 10 MPa pressureconditions and tested for the delayed fracture sensibility. As the size of investigation area is 2, 6x2, 6micrometers, the height of microrelief is achieved 0, 2 mkm. The character sizes of the secondarymicrocracks-depth is 0, 2 and width is 0, 3 mkm. The indication that the cracks are propagate by themechanism of nucleation and coalescence of such microdefects as micropores and microcracks isobtained here. On fig. 3 the break surface that similar to the pitting tearing surface and shaped by the

ruptures over the growing microdefects is shown. The size of investigation area is not exceeds 3x3 MKMand the height of microrelief is about 30 nm.

On figure 3 the surface of a secondary submicrocrack, which begins from a carbide inclusion isshown. The submicrocrack spreads along the crystallographic planes in grain body of martensite. A two-dimensional image allows to measure the parameters of the submicrocrack-it length about 2 mkm, depth

100 nm, and width 200 mm. Using a three-dimensional image and the profile the size of the carbideinclusion was determined-it length 3-4 mkm, width-about 300 nm, height-150 mkm. The

abovementioned mechanism of the microcracks nucleation on the microdefects in the form of inclusion is

peculiar to the samples, that are subject to hedrogen induced delayed fracture under the static loading,

what the shown defects indicate (see fit. 3). te distribution of thus defects and imperfections atmicrolevel and its typical sizes was used in stochastic modelling of germination on microdefects, growth

by the viscous-plastic law, and mutual coalescence of small cracks, and the subsequent of the main

macroscopic crack.

Fig. 2. The viscous fracture surface of the hydrogen saturated ë. 3. Thé secondary cracks on thé fracture surface of14H2GMP steel specimen with the traces of pitting cleavage, hydrogen saturated 14H2GMP steel specimen, x32768

x32768 magnification : 2-dimensional image, profile of the magnification : 2-dimensional image and profile of thesurface and 3D-image of the scan. surface and 3D-iniage..f.'. ? T'L c r surface and 3D-imase..surface and 3D-image ofthe scan. °

The study of ultimate states of material is directly connected to the lifetime numerical estimation

of constructions manufacture from widely used and new materials. The last investigations in this

directions are linked to the study of influence of grain boundaries and interfaces, particularly, impuritysegregations on grain boundaries, on the deformation and fracture of polycrystalline and nanostructuralmaterials. By means of electron scanning microscopy the " in situ " investigation of the evolution ofsurface damage during the deformation of small-sized specimens of the experimental cold-resistant steel

was conducted. The fitted 4, 5 kN loading device and 20x20x2 mkm tunnelling probe was used. Theresults of scanning of grain boundary before and after the 5%-deformation is shown on figures 4 and 5. Itis seen on the 3D-images and profiles that the surface relief change and the small cracks is appeared,before the extensive macroscopic plastic déformation. The damaging bas been numerically estimated bythe methods of multifractal analyses [10].

Fig. 4. Initial state of the grain boundaries of the cold-PHe. 5. The grain boundaries of the cold-resistanceresistance e xperimental steel (lOx7 nikm) : 2-dimensional steel under the 5% deformation (5x5 mkm) : 2-

scan, profile, and 3D-image of the seanning surface. dimensional scan, cross section profile, and 3D-

image.

3. MODELING PROBLEM DEFINITION

The well-known optical and image recognition methods could be used on macro and meso-level [5, 7].

The depth average data with the micro-and meso-components with separable micro and meso-components could be obtained by the x-ray fractography method. For the computer simulation of crack

growth in heterogeneous viscous-plastic material the stochastic approach bas been used. The approach

based on the mechanism of growth and coalescence of microcracks.

thermal boundary conditions, The model of grain formation is based on the

1 probability information

for combine cellular automata-finite element (CAFÉ

nucleation and cell formation model) [11], and assumed that the dendrites growth___'--- _-ismodeled on thé probability defined solidphase

F8\II modelling CAFE (Cellular germs in the melt (by cellular automata method)of sdlid cooling Automata-and thermal flow calculation in the mushy zone (byafter casting Rnite Beement) finite elements method). The grain structure with

modelling of the calculated dendrite orientation in each of grainsgrain structurej i n ra t^e and the results of macroscopic heat transfer as the

. ti@o input data for the porosity evaluation and crack

Macrosrc-opic

astres tra, nsife- propagation models correspondingly whereare ss

ad r-,,--strain fieldl----, Grainsstructure obtained in that case.

-C

t U,

e

X rl I < and dendrites) Thc conceptual scheme of the modeling ofFbrosity prediction " ctio processes that taking place during the forcing of

Nrnode ! thé part from the melt, and of the connectionsbetween thé models developed is shown on the. haction of fig. 6. Thé

FE-solution of the thermal problem ofcooling of the already solidified metal is carried out

by the program software ABAQUSO. The value

!--- ! -andrateofthesolidphasestrainthatusedinthe

model porosity evaluation model, and the strain and stressitb of fields that defined the extemal loading for the

. XRobab ! !) tyoT\ 1) t i. f <

f D [Qpagat ! On, calculation

by the stochastic crack propagationti n,ble model, is determined in that case. The result of the------ crack

propagation modeling is the probability of

Fig. 6. Conceptual scheme of the connections between the small cracks nucleation, the propagation way,models in whole modeling of hot tearing of AI-alloys. velocity and branching of the main crack. All this

parameters is depend on strength characteristicsand micro-and mes-structure of material, the boundary conditions of thermal problem (adiabatic,permanent cooling) are influence on the solution also.

4. STOCHASTIC MODELING RESULTS

The stochastic model of crack propagation in a multiphase, heterogeneous material is based on themechanism of stress induced opening of the cracks or pores at particles or flaws, its viscoplastic growthand coalescence with a main crack or adjacent pores. The crack growth in multiphase material issimulated by means of developed model based on the well-known stochastic algorithm proposed byB. Broberg [12].

It is assumed that thecoordinates of maincrack or initial pore and

the mean values offraction of pores and its

t'r--- are known from theD experimental data, but

have a stochasticprobability nature.According to scheme onthe fig. 6, the grain

Fig. 7. The results of the calculation by the stochastic model of crack propagation in boundary (as a mostviscous-plastic micro-defect material probable area of the

pores'nucleus distribution) is given numerically by CAFÉ model, the fraction of pores is given by theporosity model, and the stress fields are given by the ABAQUS software calculation.This model is essentially bas the same features as described in [12], except the effect of hydrogen and thepossibility o f changing the deformation and growth government e quations (for e xample, for t he s mallcracks growth description).

On fig. 7 the result of calculations by the stochastic model of crack propagation in viscous-plastic micro-defect material in cases of randomly homogeneous distributed microdefects and correspondingmesocracks. In all cases the average defect size was 2 mkm, yielding 730 MPa, the tension load

0. 5characterized by the stress intensity factor in the main crack tip about KI = 60 Mua M-

5. ACKNOWLEDGEMENTS

Authors are indebted to colleagues at the Material Department of the Swiss Federal Institute ofTechnology Lausanne (EPFL), especially to prof. Michel Rappaz and prof. Wilfried Kurz, for theirassistance in numerical modelling on ABAQUS il CAFÉ software, assistance in porosity model building,and for the discussions of results.

The support of the Russian Foundation for Basic Research (Grant No. 01-01-00161, Grants No. 03-01-96000 and 03-02-96000 " Arctic program ") and Integration Complex Program (Project No. 2) of SiberianDepartment of Russian Academy of sciences is gratefully acknowledged.

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