New experimental procedure for analysis

Tiré à Part

N ew experimental procedure for analysis of rivets material mechanical properties

L. Patronelli, B. Langrand, E. Deletombe, E. Markièwicz*, P. Drazètic*

Crash questions (CEAS)

N aples (Italy), February 14-16, 2000

NB : Ce document comporte 12 pages

Ce Tiré à part fait référence au Document d’ Accompagnement de Publication DMSE0002

N ew experimental procedure for analysis of rivets material mechanical properties

N ouvelle procédure pour l'analyse des propriétés mécaniques du matériau constituant les rivets

par

L. Patronelli, B. Langrand, E. Deletombe, E. Markiewicz*, P. Drazétic*

* UMR CN RS 8530 (Mechanical Engineering Research Group) Université de Valenciennes (France)

Crash questions (CEAS)

N aples (Italy), February 14-16, 2000

Résum é

Résum é : L'analyse par élément finis de la tenue des assemblages rivetés nécessite la connaissance des lois de comportement. N éanmoins, la petite taille des rivets (8 mm de long) ne permet pas de procéder à des essais de traction classiques pour caractériser proprement la loi de comportement du matériau rivet.

NEW EXPERIMENTAL PROCEDURE FOR ANALYSIS

OF RIVETS MATERIAL MECHANICAL PROPERTIES

L. Patronelli, B. Langrand, E. Deletombe, E. Markièwicz¥_{, P. Drazètic}¥ Department of solid and damage mechanics, Structural resistance and design section,

ONERA-Lille, 5 Bvd Paul Painlevé, 59045, Lille, France. Email : patronelli@imf-lille.fr. ¥ Industrial and human automatic control and mechanical engineering

laboratory, Mechanical engineering research group (UMR CNRS 8530), University of Valenciennes, Valenciennes, France

Abstract: The study of airframe crash behaviour becomes a necessary step in aircraft design (for possible future certification requirements). An airframe is composed of many parts (e.g. skin, frame, stringers, clippers) mainly assembled using riveting techniques. These complex assemblies lead to several basic non-linear rupture phenomena observed in case of crash events. Since 1995, the ONERA-Lille Research Centre and LAMIH from the University of Valenciennes have been leading numerical and experimental basic studies to analyse local material and global joints behaviours and improve the riveted joints design. The final objective is to model full scale crash events using accurate but macroscopic FE joints models.

Intrinsic material laws have to be characterised to perform numerical analyses of the joint strength. Nevertheless for the rivet materials, it is impossible to undertake uniaxial tensile test using classical specimens because of the small size of the rivet itself (8mm, long). To give access to the rivet material law, the ONERA-Lille Centre has developed an original micro-tensile test rig. In the first part of the paper, experiments are performed on a AU4G-T4 aluminium alloy. Results obtained with the new procedure and with the classical uniaxial tensile test are compared to validate the micro-tensile test concept. In the second part, the rivet material (7050 aluminium alloy) is then characterised with the new test rig.

The riveting process introduces residual stresses and plastic strains (> 5%) into the rivet (which comes from the compression loading). So the objective of the third part of the paper is to highlight the influence of compression residual plastic strains on the rivet material behaviour when tensile load is applied. First, rivets are crushed to introduce compression plastic strain (about 5%). Second, micro-tensile specimens are manufactured from the crushed specimens and micro-tensile experiments are undertaken. Results are then compared with the compression and tensile material laws of the 7050 aluminium alloy to highlight the influence of kinematic hardening on the mechanical properties of this material.

This experimental work would prove to be useful to accurately improve the design of new riveted joints techniques. An original experimental procedure has been developed to characterise material parameters and to analyse kinematic hardening effects on material laws. The ultimate aim of these studies is also to improve the joints F.E. models for airframe crashworthiness

Keywords : Tensile test - Riveted joints - Characterisation - Kinematic hardening Notation :

Latin

A,B,n power model parameters E Young modulus

Fmax maximum load

SN Gaussian standard deviation

Vimp loading velocity

f(zi) convergence criterion

fc critical void volume fraction at coalescence

fF critical void volume fraction at ductile fracture

fi initial void volume fraction

qi porous material parameter

zi parameter vector Greek.

εN nucleated effective plastic strain

σe. yield stress

σmax. maximum stress

δres residual displacement

1. INTRODUCTION

An airframe is composed of many parts (sheet metal plates, beam...), assembled by riveting techniques. The aim of crash studies is to improve the behaviour of airframe in term of energy absorption and cabin deformation. These studies are leaded with numerical tools which decrease cost compared to experimental procedure [1].

Before performing this kind of complex crash study it is necessary to characterised the rivets macroscopic behaviour (non-linear behaviour, failure criterion) [2]. Indeed, airframes are built with numerous rivets which influence the ruin mechanisms in case of crash [3], but it is impossible for obvious reasons of computing costs to refine the mesh at the rivet geometrical level in airframe models [4]. For this reason, thin simulations of rivets under mixed mode loading are previously undertaken and lead to the determination of different parameters for simplified link models (equivalent elements proposed by FE codes) [5]. To compute this kind of thin simulations, the behaviour of the crushed rivets material must be known up to failure (eg. Gürson damage model). Previous works have shown the high plastic strain level which develops in rivets during the forming process (εp from 5% up to 17% [6]). This is the

reason why it is proposed to characterise the effect of this first loading (riveting process) on rivet material, to be used in simulation (and more particularly the use on kinematic or isotropic hardening).

For that purpose, it is proposed to develop a new experimental characterisation technique which consists in doing micro-tension tests : indeed the size of rivets, which are about 8 mm long, raises problems considering classical characterisation techniques. First, it is impossible to use a normalised tension test specimen (l=5.65√S). Second, the geometry of the test specimen must be specifically designed for this kind of application. Third, it is necessary to use and adapt micro-gauge to measure the strains. As a first step, numerical tools help to select the geometry of the test specimen. Then the experimental investigation is divided in two steps. A first validation of the experimental procedure is presented by comparing test results with classical available ones on AU4G-T4 aluminium alloy. Then other tests are performed on “ on the shelf rivet ” extracted test specimens. Both results permit to undertake an identification of damage parameters of Gürson’s model with an inverse method (optimiser coupled to FE code Pam-solidTM [7]).

2. DESIGN OF TEST SPECIMENS GEOMETRY

2.1 GEOMETRICAL CONSTRAINTS

In the present case, the aim is to extract a test specimen from the rivet itself (small size of the rivet). The raw material available to manufacture the test specimen is a 4 mm diameter and 8.2 mm long cylinder. A test specimen is usually designed with two different parts. A working part where the material behaviour is captured (elasticity, plasticity, damage) during the loading phase. A second one which permits to attach the test specimen to the tensile machine. Considering the very small size of the specimens, we must consider a third one, which is the area between the two previous ones, in which geometrical effects may amplify and interact with the working part behaviour [8]. The objective is to take care about and minimise local embrittlement and stress concentration phenomena in that area if necessary.

The final diameter of the working part of the specimen is chosen equal to 2 mm. Total length of test specimen is still 8.2 mm and it is proposed to use a working length of 1.5 mm. The final test specimen is shaped by turning process (better machined tolerance in this case). The grip system between the test facility and the specimen is a self-closing system (Figure 1).

Two shapes for the junction area are investigated (chamfer or junction rounding-off , see Figure 1). To check and choose between the two solutions, a F.E. code is used.

2.2 INFLUENCE OF THE JUNCTION AREA SHAPE

Both presented simulations are realised with an explicit FE code Pam-SolidTM. The nodal boundary conditions and the modelling simplifications are presented on Figure 2 (only 1/8th of the geometry is modelled). A rigid body is defined to model the massive parts (grip system). The master node of this rigid body is pulled by a rigid wall, the displacement of which is imposed by a velocity curve Vimp= f(t). The use of such a

rigid body gives access to the global load and displacement. In the first simulation, the junction area is a chamfer (α=60°). In the second, it is a junction rounding-off (r=2.12 mm).

The constitutive material law which is used is described as a power-model (hardening behaviour) coupled to the Gürson damage model (softening behaviour). Since the aim of this part of work is just to compare both specimen geometry response, Gürson damage parameters are taken from the literature [2].

Figure 3 shows the Von Mises stresses obtained in both simulations. Plastic strains are localised in the working part and no stress concentration phenomenon in the area of separation between working length and junction area is observed. Figure 4 gives the global load versus local strain. Finally the smallest deviation obtained between both curves shows that it is possible to take the simplest geometry for the specimens to be tested (chamfer instead of junction radius).

3. EXPERIMENTS

3.1 DESCRIPTION OF THE NEW PROCEDURE

Figure 5. Micro-gauges (L=0.5mm, h=0.38mm) are used and bonded in the working length area to measure directly the material deformation. This kind of micro-gauges can catch up to 20% strain levels before failure. The global load F is measured with a piezo-electric load cell (Kystler 9077). The displacement of the rigid rig is measured on the Schenck G-Nr 911 test facility sensor.

Quasi-static and dynamic tests performed on single lap riveted joint test specimens have highlighted no influence of strain rates on global behaviour and failure mode of the assembly (failure of 7050 aluminium rivet) [9]. As this step of the study, we will then consider for simplicity a quasi-static load velocity of Vimp =0.2mm/min.

To validate the experimental procedure and check if the specific geometry of the test specimens enables us to get intrinsic mechanical properties of the material, a first series of test specimens is realised in a well known aluminium AU4G-T4 [10].

3.2 TESTS RESULTS

3.2.1 AU4G-T4 aluminium alloy

Results are presented in Table. 1 in terms of Young modulus, maximum and yield stress. Figure 6 shows the load versus displacement diagram for the AU4G-T4 aluminium alloy (the error linked to the setting of test specimens is corrected on the diagram). In fact the linear elastic behaviour is extrapolated on the basis of the measured behaviour between 0.07 and 0.1 mm of displacement). The obtained results show that AU4G-T4 aluminium alloy is slightly ductile. The local variables are presented on a stress-strain diagram in Figure 7 (real stress versus effective plastic strain). Global and local results show that the experimental procedure is validated in comparison with the literature for the AU4G-T4 aluminium alloy, except for the maximum stress which is known to be specimen sensitive.

Table. 1 Mechanical characteristics of AU4G-T4 aluminium alloy.

Source E (MPa) σmax (MPa) σe (MPa) Α%

micro-tension 75000 465 300 18

Literature [19] 74000 420 280 18

deviation % 1.35 9 6 0

3.2.2 7050 aluminium alloy

Results are presented in Table. 2 in terms of ultimate load and total displacement at failure (measured on test specimen after failure). The yield stress and the maximum stress σy and σmax are also reported in Table. 2. Figure 6 shows the load versus

Table. 2 Tests results (7050 aluminium alloy).

7050 F_u (kN) δ_res (mm) σ_e- (MPa) σ_max (MPa)

test_1 1 0.56 329 530

test_2 1.1 0.53 325 520

test_3 0.97 0.61 315 508

test_4 0.92 0.62 320 510

Average 0.9975 0.58 322.5 517

3.3 SYNTHESIS

The micro-tension test has been used to characterise two aluminium alloys (7050 and AU4G-T4). The mechanical properties of the AU4G-T4 aluminium alloy obtained from the micro-tension tests enable to validate the experimental procedures. It proves its capacity to characterise constitutive material law for rivets in tension (or more generally small pieces).

The tests performed on 7050 aluminium alloy show the more ductile property of this aluminium. The obtained local results (stress-strain curve) permit to identify parameters of a power-model for εp<5% (with the assumption that no damage

develops for εp<5%). Only the load versus displacement diagram gives access to the

material behaviour up to failure (micro-gauges are limited to a 20 % deformation). Hence, the identification of Gürson’s model damage parameters is then undertaken on this response using an inverse method.

For a loading velocity of about 2mm/min the measured strain rates are in the order of magnitude of 0.02 s-1. So strain rates of about 600 s-1 (strain rate level interesting for crash scenarios) could be expected with this specimen geometry and loading velocities equal to 1m/s.

4. IDENTIFICATION OF GÜRSON MATERIAL MODEL

PARA-METERS [11-18]

4.1 OPTIMISATION TECHNIQUE

At a first run the optimisation procedure deals with the power-model parameters (σ = A+Bεp

n

). These parameters are computed for a range of deformation less than 5 % (no damage develops in this range). The identification is made with a direct method, taking 322.5 MPa as the yield stress A. The final values obtained for B and n are respectively 595 and 0.35 (Figure 11).

Where Np represents the number of experimental measurements of quantity ωexp. The load versus displacement response is used to perform the identification. The general identification method is based on physical considerations concerning the targeted parameters (chronology of events). So, at a first step, parameters εN, fN, SN

and fI are optimised. Then parameter fC, which is the critical void volume at

coalescence, and finally fF, which is the critical void fraction volume at ductile fracture,

are computed. Parameters qi concerns the micro-voids geometry. It proves to

influences the three steps of damage. The identification process is initialised by parameter vector z={q1, q2, fI, fN, SN, εN, fC, fF}={1.5, 1.5, 1E-17, 0.045, 0.075, 0.15,

0.045, 0.055} given in literature for the 7050 aluminium alloy [2]. Computing time is about 15 minutes on HP9000C100.

4.2 OPTIMISATION RESULTS

Finally, after 30 optimisation cycles, the parameter vector obtained is z={q1, q2, fI, fN,

SN, εN, fC, fF}={1.15, 1.5, 1 E-17

, 0.042, 0.075, 0.2, 0.165, 0.175}. Only the parameters q1, fN, εN, fC, and fF have changed. The reduction of q1 value means a more elliptic

micro-void geometry than initially.

The critical void volume at coalescence, fC, and the critical void fraction volume at

ductile fracture, fF, are more important than in the literature.

Figure 12 shows results in terms of loading versus displacement diagram and von Mises stress. Displacement at failure and maximum load are well predicted. Moreover the non linear behaviour is better apprehended with this newly identified model.

5. INFLUENCE OF RESIDUAL STRAINS ON GLOBAL LOAD

RESPONSE

5.1 EXPERIMENTAL PROCEDURE

To introduce residual strains of about 5% in the test specimen it is necessary to proceed in 3 steps :

• extract a cylinder (φ=4mm, h=8mm) of a 7050 aluminium rivet,

• crush the cylinder to reach εp=5%,

• machine a test specimen in the crushed cylinder.

The residual strain level of about 5 % corresponds to the mean level observed in 7050 aluminium rivet beam after being riveted, in respect with craft rules (see Figure 9) [20-21]. With this method, it is now possible to investigate the influence of residual strains on global material behaviour (F, δ). Results are given in a conventional diagram (A%,

σ=F/S0).

5.2 RIVETED MATERIAL DATA

Figure 10 compares results obtained with both experimental investigation (with and without residual stress in 7050 test specimens). In its natural state, the 7050 aluminium alloy has the same yield stress in tension and compression. The forming process modifies the tension characteristics of this aluminium as follows :

• mechanical characteristic decrease (σe0.2 = 200 MPa and σmax = 420 MPa),

• little influence on the hardening curve general shape,

The results as a whole prove that the hardening of the 7050 aluminium alloy is a kinematic one. This is mainly highlighted by the yield stress which decreases after one cycle of compression/tension. These results confirm the prediction made after ARCAN tests [5], for which the specimen strength was less than the simulated one (with an isotropic hardening model).

5.3 SYNTHESIS OF RESULTS

A residual plastic strain of about 5% is introduced in 7050 aluminium alloy test specimens. This strain level is the same as the one which can be measured in the core of rivets after the riveting process. The new test specimens (once crushed) present a yield stress of 200 MPa compared to 322.5 MPa for the natural rivet material state. The maximum stress decreases from 517 MPa down to 420 MPa. The experimental investigation shows the great influence of kinematic hardening on material behaviour and proves the need of kinematic hardening law in FE.codes.

6. CONCLUSION

An original micro-tension test technique is developed to give access to tensile constitutive material laws for small size pieces (eg. 8 mm long 7050 aluminium alloy rivets).

In a first step a validation of the experimental procedure is undertaken with well known AU4G-T4 aluminium alloy material based specimens. The obtained results (σy = 310 MPa, σmax = 477 MPa, A% = 18% et E = 75000 MPa) are compared with

the values available in the open literature. It shows no real influence of the test specimen geometry on the material law.

Micro-tension test specimens are then machined in the core of 7050 aluminium alloy rivets. Test results enable to find new parameters of the Gürson material law available in PAM-SOLIDTM F.E. code (elasto-plastic model coupled with damage model). In the one hand hardening parameters are computed with a direct method. In the other hand, parameters of Gürson’s damage model are reached using an inverse method (coupling an optimiser OPTB2L with Pam-SolidTM). The final vectors of parameter are :

• z = {A, B, n} = {310, 595, 0.35},

• z = {q1, q2, fI, fN, SN, εN, fC, fF} = {1.15, 1.5, 1E-17, 0.042, 0.075, 0.2, 0.165,

0.175}.

Other tests are then performed after having introduced a residual plastic strain state of about 5%. This strain level corresponds to the mean value measured in the core of 7050 aluminium alloy rivet after the riveting process. The new test specimens show a decrease of yield stress and maximum stress compared with material in natural neutral state. The experimental investigation proves that the hardening behaviour corresponds to a kinematic one which must be taken into account in F.E. material law used to simulate the riveted joints strength. The earlier development of damage may be the result of the natural embrittlement of material, due to irreversible evolution of microvoid geometrical characteristics (more elliptic).

It is then possible to describe the material behaviour as a coupled elasto-plastic damage model such as Gürson’s one. Before numerically characterising the static and dynamic strength of riveted joints (aluminium 7050) one should still :

• used a material law which takes into account kinematic hardening.

Under these two conditions, it will be possible to simulate correctly a riveted assembly and to evaluate the sensibility to the load velocity.

ACKNOWLEDGEMENT :

This research was carried out with an ONERA grant (operation number 99226). The authors are grateful to the ESI Group for the Pam-SolidTM FE code. The authors also wish to thanks the DASSAULT AVIATION Company.

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Figures

Figure 1. Self closing system & technologic solution for junction area.

Chamfer Junting rounding off

Technologic solution

R=2.12 mm

60°

Figure 2. Simplification and modelling (1/8th _{test specimen).}

Rigid body Vimp Master node

Rigid wall

X Z

X Y

Figure 3. Influence of junction area on von Mises stress distribution.

rounding off

5 0 1 2 5 2 0 0 2 7 5 3 5 0 4 2 5 5 0 0 5 7 5 6 5 0

Chamfer Figure 4. Global load versus stress.

0 50 100 150 200 250 300 350 400

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Strain

Global load N

Figure 5. Geometry of micro-tension test specimen.

Figure 6. Load versus displacement curve (7050 & AU4G-T4).

0 200 400 600 800 1000 1200 1400 1600

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

Dis p l a c e m e n t m m

Global load N

aluminium AU4G-T4 aluminium 7050

Figure 7. Stress-strain curve (7050 & AU4G-T4).

0 100 200 300 400 500 600

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18

Plastic strain

Stress Mpa

aluminium AU4G-T4 aluminium 7050

Figure 8. Failure mode of 7050 aluminium alloy test specimen

7050 _Rivet AU4G-T4

Figure 9. Riveting process (maximum stress state)

Figure 10. Kinematic hardening

-600 -400 -200 0 200 400 600

-10 -5 0 5 10 15 20 25 30 35 40

global strain A%

global stress MPa

crushing w ith residual plastic strain w ithout residual plastic strain

Figure 11. Identification of power model parameters

0 100 200 300 400 500 600

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2

Plastic strain

Stress Mpa

aluminium 7050 power-model

Figure 12. Optimisation results (Load versus displacement and von Mises stress) Power

model

Influence on yield stress tension

compression 300<σσ<500MPa

0 200 400 600 800 1000 1200 1400 1600

0,0 0,2 0,4 0,6 0,8 1,0 1,2

displacement mm

Global loadt N

experiment open literature parameters new Gurson damage parameters