Modèles thermomécaniques de grenaillage by Rouquette Sébastien, Rouhaud Emmanuelle, Pron Hervé, François Manuel, Bissieux Christian & Roos Arjen Université de Technologie de Troyes, Université de Reims 1
Why? Mieux comprendre les phénomènes physiques associés à la création des contraintes résiduelles Il n existe pas d évaluation des phénomènes thermo-mécaniques pour le grenaillage Quelles est l influence des phénomènes thermiques sur les contraintes résiduelles Comparaisons modèles/expériences pour validation. 2
Plan 1. Modèles et résultats numériques 2. Experimental device & données 3. Comparaison/Discussion 4. Conclusions & perspectives 3
Thermo-mechanical modelling Assumptions : Axi symetric p, Dynamical study, Normal shot impact, Elastic steel shot, Thermo-elasto-plastic plate with isotropic hardening plastic model Shot diameter and velocity : 4,5 mm & 80 m/s, The thermo-mechanical coupling : & T " C p ' ( # ( = $ % & t p ( T )! ( : )! 0.8<b <1 (Rosakis & al, 2000) 4
Model massif semi infini Shot 200 C 200 C 177 C 0.3 mm Semi infinite Body Point A Limit of the plastic zone 155 C 132 C 110 C 87 C 65 C 42 C 20 C 5
Contraintes résiduelles et rayons de billes massif semi infini 6
Contraintes résiduelles et vitesse de billes Massif semi infini 7
Experimental device & data Experimental & measurement devices : Temperature measurement by infrared camera Pneumatic ejection system Experimental chamber Clamped 316L steel plate i.r. view of the plate rear side Speed camera I.R. camera 8
Experimental device & data Experimental measured temperatures (estimated shot velocity ~ 80 m/s) : 29 28,5 Temperature ( C) 29 28,5 Temperature ( C) 28 28 27,5 27 26,5 Centre Zone 1 Zone 2 Zone 3 27,5 27 26,5 Centre Zone 1 Zone 2 Zone 3 26 Time (s) 25,5 0,5 0,75 1 1,25 1,5 1,75 2 0.25 s 0.25 s 26 Time (s) 25,5 0,5 0,75 1 1,25 1,5 1,75 2 ~8 mm Temperatures computed on three defined zones, 2 shot impacts give same temperature rise ~ 2.7 C, Temperature rise peaks appear 0.25 s after impact, Defined thermal zones 9
Thermo-mechanical modelling Z! SHOT Heat exchanges Symmetry axis PLATE No vertical displacement r! Boundaries conditions 10
Thermo-mechanical modelling and numerical results Symmetry axis Numerical results : Z! SHOT Heat exchanges PLATE No vertical displacement I.R camera Boundaries conditions r! T(z) T(r) 108 C r = 1,5 mm Limit of the cumulated plastic deformation Temperature field at the maximum penetration of the shot (t~8 µs, 80 m/s) 110 C 99 C 88 C 76 C 65 C 54 C 42 C 31 C 20 C 11
Thermo-mechanical modelling and numerical results Symmetry axis Numerical results : Z! SHOT Pt1 Pt2 & Pt3 Heat exchanges PLATE No vertical displacement I.R camera Boundaries conditions r! point 1 90 80 70 60 50 108 C r = 1,5 mm 40 30 20 temperature rise ( C) pt1-80 m/s* pt1-70 m/s* pt2-80 m/s* pt2-70 m/s* pt3-80 m/s* pt3-70 m/s* Limit of the cumulated plastic deformation Temperature field at the maximum penetration of the shot (t~8 µs, 80 m/s) 110 C 99 C 88 C 26 76 C 25 65 C 54 C 42 C 31 C 20 10 100 1000 10000 100000 1000000 log(time) (in microsecond) 27 24 23 22 21 20 C 12 point 2 & 3
Thermo-mechanical modelling and numerical results Symmetry axis Numerical results : Z! SHOT Pt1 Pt2 & Pt3 Heat exchanges PLATE No vertical displacement I.R camera Boundaries conditions r! temperature rise ( C) 110 100 90 80 70 60 50 40 30 20 T(r) - 80 m/s* T(r) - 70 m/s* 0 0,25 0,5 0,75 1 1,25 1,5 radius (distance to symmetry axis in mm) Temperature field at the maximum penetration of the shot (t~8 µs, 80 m/s) 13
Thermo-mechanical modelling and numerical results Symmetry axis Numerical results : Z! SHOT Pt1 Pt2 & Pt3 Heat exchanges PLATE No vertical displacement r! temperature rise ( C) 90 80 70 60 50 40 30 20 T(z) - 80 m/s* T(z) - 70 m/s* 0 0,5 1 1,5 2 2,5 3 depth (distance to the surface in mm) I.R camera Boundaries conditions Temperature field at the maximum penetration of the shot (t~8 µs, 80 m/s) 14
Numerical results : Thermo-mechanical modelling and numerical results Residual radial stresses (MPa) 800 600 400 200 0-200 0 0,5 1 1,5 2 2,5 3 distance to the surface (mm) Effect of the heat on the residual stress: thermo-mechanical simulation* and mechanical simulation** 80 m/s* 80 m/s** 70 m/s* 70 m/s** 15
Comparaison temperature rise ( C) 30 29,5 29 28,5 28 27,5 27 26,5 26 Centre point 1 pt1-70 m/s* pt2-70 m/s* 0,8 1 1,2 1,4 1,6 1,8 2 time (s) 16
3. Conclusions - Perspectives Conclusions : A experimental device has been developed to measure the heating of a plate impacted by a steel shot (D T~2.7 C in our experimental conditions) A thermo-mechanical modelling of the experiment has been made Comparisons between experimental and numerical thermal curves are in good agreement More : the thermal problem uses an inappropriate parameter b : & T " C p ' ( # ( = $ % & t p ( T )! ( :! ) a better formulation will be more suitable (including internal variables): T! C & ' ( " ( T = #! $ ' Rp ' X %! p ( ) :! : p ) ) & t 17