The new features of Photothermal Prospecting as a Non- Destructive Testing technique applied to steel surface-treated alloys.
Taher GHRIB Équipe Photothermique de Nabeul I.P.E.I.N. Merazka, 8000 Nabeul. TUNISIA e-mail :
[email protected] Karem BOUBAKER École Supérieures des Sciences et des Techniques de Tunis / 63 Rue Sidi Jabeur, 5100 Mahdia. TUNISIA e-mail :
[email protected] Mahmoud BOUHAFS Unité de recherche MA 21 Ecole Nationale d’Ingénieurs de Tunis B.P. 37 Le Belvédère 1002 Tunis - TUNISIE e-mail :
[email protected] Noureddine YACOUBI Équipe Photothermique de Nabeul I.P.E.I.N. Merazka, 8000 Nabeul. TUNISIA e-mail :
[email protected] Abstract This study sums up the authors recent works] on steel Non-Destructive Testing and Evaluation achieved between 2000 and 2008. The main related items are the establishment of a first-order correlation between the thermal diffusivity and the Vickers hardness HV as a guide to set an NDT protocol to investigate steel strengthened surface performance. A special attention is confined toward carburized steel material, as the existence of any appropriated NDT photothermal technique is demonstrated to be unavoidably subjected to some restrictive conditions. The perspectives of the new features of this recent technique are discussed, with special concern with differently treated material like nitrured and nitrocarburazed quenched steel. Keywords : NDT, Thermal diffusivity, Vickers hardness, Photothermal techniques, Treated steel.
Résumé La présente étude résume les travaux récents des auteurs sur les essais et l’évaluation non destructifs effectués sur les aciers entre les années 2000 et 2008. Les principaux axes développés sont l'établissement d'une corrélation de premier ordre entre la diffusivité thermique et la dureté Vickers HV comme guide pour établir un protocole de NDT pour étudier l'acier renforcé en surface. Une attention particulière est portée sur les travaux concernant l’acier cémenté, puisque l’on a démontré l’existence de conditions restrictives à l’application des techniques photothermiques. Les perspectives de l’application de cette technique récente sont discutées, avec une orientation privilégiée vers les alliages différemment traité (aciers nitrurés, nitro-cimentés et trempés). Mots-clés : NDT, Diffusivité thermique, Dureté Vickers, Techniques Photothermiques, Acier traité.
1. Introduction Testing the surface performance of hardened steels is a major issue in mechanical and metallurgical industries. Steel surface hardening procedures are commonly quenching , carburizing, nitruration or Laser local treatment[1-10] ; these procedures leads always to higher properties as bettering surface hardness or notch toughness of common used device (tools, shafts ...). Specially, low carbon alloyed steels Laser heating presents an efficient prelude to austenization since small targeted volumes can be treated apart. However, evaluating treatment efficiency faces a lot of problems due to mechanical testing process, based on hardness measurement which are mainly destructive and need a costly sampling. In this context, photothermal depth profilometry has been presented, during the last decades, as a thermal-wave inverse-problem technique that reconstructs a given material thermal diffusivity profiles from experimental surface data. As thermal characteristics depend on microstructural and mechanical properties, monitoring them yields information on changes that occur as a result of surface modification. The remaining problem is the investigation of the correlation between these thermal parameters and mechanical one. This correlation is the single way for validating the use of any non destructive technique. Several recent studies [1-12] have tried to establish a correlation between thermal diffusivity and microhardness. Jaarinen et al. [13,14] prospected the variation of thermal diffusivity with depth inside metallic samples. They could detect some local defects with a good accuracy. The works of Busse et al. [15,16] extended the use of the photothermal techniques to several materials. Their yielded results confirm the suitability of the technique when applied to steel and metallic samples. In this paper, we try to confirm a further conjecture [2,5,6] about the validity of a linear first-order correlation between thermal diffusivity and microhardness. In fact we established a prior condition to this correlation that traduces changes in material composition rather than structure. Nicolaides et al. [16,17] concluded in their last studies that when a steel sample is subjected to a carburizing treatment followed by quenching, the thermal diffusivity profile is dominated by carbon diffusion during carburization, while the absolute thermal diffusivity values are dominated by microstructural changes that take place during quenching. The same authors stated that the validity of these conclusions for other types of steel is uncertain. As the correlation was not justified in quenched or annealed samples, we had to measure the characteristics of samples submitted to treatments that mainly alters chemical composition. The main targeted material was hence carburized steel. Our present study presents recent results and analysis obtained by using nitrured steel samples. The existence of the proposed first order correlation is confirmed.
2. The Photothermal techniques for NDT purpose 2.a The indicial response techniques It is known that when a body receives a single heat pulse from distant source, it acts temporarily as a local source. An adequate detecting sensor, located at a predefined position regarding the targeted surface (fig. 1.a) will record a response whose form, amplitude and duration depends on the material properties. The major disadvantage of the indicial techniques [9-11] is the lack of repeatability. In fact successive excitations may cause unexpected correlation between measured values. Since thermal characteristics are usually temperature-dependent, the yielded values would vary unless a long time is ensured between two consecutive applied pulses.
2.b The frequencial response techniques The frequencial response technique differs basically from the indicial ones. In fact, they are based on the response to a continuous modulated excitation (fig. 1.b). A source provides at each period an energy whiff which is appropriately directed toward the targeted surface. The detection device must be adjusted to the modulation frequency, the manner that the detected signal is attributed exclusively to the excitation effects. Generally, the generated signal is detected in the fluid in vicinity of the targeted material [1-8]. The known phenomenon of heat-induced reflection index variation (Mirage Effect) is also experienced [1-6] in this technique.
3. Theoretical support 3.a Analytic derivation of surface temperature expression It is known that when a body is heated by a distant source (figure 1.b), and when a determined fluid separates source from target, incident energy flow induces, inside the bulk fluid, a temperature gradient expressed [2,3] by the equation (1):
(1)
f = -k s .grad (T )
where ks is the body thermal conductivity (W.m-1.K-1) and T is the absolute temperature (K). We can approximate the excitation beam by a Gaussian beam, the heat energy transmitted from the target to the fluid per unit volume, and at a pulse frequency f is hence expressed by the equation (2); -
r² b ² e - jwt
(2) Q (r , t ) = Q = Q0 .e where Q0 is the nominal heat transmitted from the target to the bulk fluid elementary volume, whose value depends on both fluid and targeted surface thermal parameters, w = 2pf, and b is Gaussian beam external radius Ñ 2T -
Q 1 dT . =- v D dt ks
with D =
(3)
ks , the thermal diffusivity of the material (in m2s-1) r .C
The equation (3) is solved using Henkel direct and inverse transforms[4-6]. We obtain finally (4): r2
- 2 I T (r ,0) = 0 e b (4) a .k s This expression is compatible with the result proposed by Murphy et al. [18], and traduces a perfect superposition of the surface temperature profile Ts(r) on the beam one. This superposition of thermal and optic spots is attributed, according to the same authors, to the slowness of modulated thermal energy diffusion inside a thick material. An other study showed [19] that in the in the case of a pulsed Gaussian beam at a frequency f, it is necessary to take in account, in addition to the temporal component, the thermal wavelength lth in the material. The expression of the surface temperature then is (5):
-
I0 Ts(r,0,t)= .e a.ks
r2 2
2 b +lth
.e- jw.t
(5)
3.b Photothermal deflection signal parameters The normal and radial components of the probe beam deflection, respectively yz and yr are calculated [5,6] by the relation (6): +¥ ö æ 1 ¶T ÷ ç (6) ÷ T0 ¶z æy z ö ç ÷ (y ) = çç ÷÷ = ç + ¥ 0 ÷ èy r ø ç 1 ¶T cos q .dl ÷ ç ÷ ç T0 ¶r 0 ø è
ò
ò
where dl presents probe beam geometrical path, and T is defined by Equation (5). In the case of optically thick massive sample heated by Gaussian beam source; theoretical calculations of probe beam deflection components yz for a small offset z0, give (7): I c + c.bh 2 -s f ( z0 -h) -jwt yz = 0 b2+l th e e T0a.k s (bh -1) + c(bh +1) (7) = y z .e
-jwt + f z
In the case of the prospected steel samples, theoretical calculations of probe beam deflection components yz for a small offset z0, give eq.(8-9): z ö æ - 0 ç I0 l th , fl -jwt ÷ 2 2 l b + e e th , s ÷ æ y .e -jwt + f z ö ç y ÷ ÷=ç z (y ) = æçç z ö÷÷ = ç T0a .b.k (8-9) z0 ÷ ç w f -j t + y ÷ ç y .e r ÷ è rø ç I r l w ø è -j t 0 ÷ ç e th , fl e ÷ ç T0a .k ø è With the definition lth,fl = (j.Dfl/pf)½, we obtain the system of deflection components (10-11): 2 p.f ì 2 ). z0 -( I D 2 D fl 4 0 ïy z = b + 2 s 2e ï T0a .b.k p .f í Ds ï p 1 p. f 2 ïf z = - 4 + 2 arctan(p . f .b 2 ) - ( 2 ).z 0 D fl î
(10-11)
Theoretical k-dependence of |yz|,|yr|,fz and fz as functions of modulating frequency f is the main support of next investigations. 3.c Determination of the thermal diffusivity and conductivity of the samples According to the expressions (eq. 10-11), conjointly with the theoretical variations of the slope S of the curve for high frequency values is given by eq. (12-13) :
Ln(y z
)
f ® +¥
@ -(
2 2 p. f é p ù ).z 0 = ê - ( ).z 0 ú f =S´ 2 2 D fl êë D fl úû
f , S = -(
2 p ).z 0 (12-13) 2 D fl
The calculation of the slope S, in addition to accurate knowledge of air mean thermal diffusivity air Dfl leads to obtaining the offset z0 ; whose value is difficult to measure experimentally. Subsequently, and using the expression (eq.12), we determine the coordinates Ln(AM) and fM of the medium range point M (MRP). This point is chosen so that low frequency perturbations and high frequency noise are avoided (fM=64Hz). As the slope S is already known, the value of the thermal diffusivity Ds of the sample is deduced from the value of fM; and (eq. 13), with given value of b: ö æ p Ds = p . f M .b 2 . tançç 2æç f M + - S f M ö÷ ÷÷ (14) 4 øø è è The value of the thermal conductivity ks of the sample is then obtained using the lastly calculated value of thermal diffusivity Ds and (eq. 12): 1
æ ç
- Ln ( AM )+ Ln b I0 4 çè ks = e T0a .b
4
+
Ds2 ö÷ +S p 2 . f 2 ÷ø
fM
=
I 0 e S fM D2 ´ 4 b4 + 2 s 2 T0a .b AM p .fM
(15)
4. Correlation between the thermal diffusivity and the Vickers hardness 4.a Case of the carburized steel The correlation between hardness and thermal diffusivity was experimentally determined [4] by a photothermal method, applied to several carburized steel samples. A second study tried to establish the limits and the extents to this correlation [6]. Figure 2.a. yields conjoint thermal-mechanical profiles inside differently treated samples. The monitored correlation (fig. 2.b) was noticed regardless further treatment (quenching, annealing..).
4.b Case of the nitrured steel We tried, in a precedent study [6], to prove that the linear correlation between the thermal diffusivity and the Vickers hardness HV is attributed to composition change during treatment rather than structural changes. For this purpose, we had to induce a different composition change (i.e.) nitruration. The nitruration consists of the diffusion of the nitrogen ions N+ inside steel samples under standard conditions. We used 42CD4 steel cylindrical samples which we submitted, individually to the following cycle: - The sample was first placed in an ammonia-rich atmosphere furnace set initially at room temperature. The gas-sample unit was heated gradually until ammonia cracking temperature (T=520°C). - The temperature was kept constant with 520°C for a given duration (T1=24h, T2=30h orT 3=36h). During this stage the ions N+ diffuse gradually inside the sample - Finally, a progressive Cooling phase was held until the temperature T = 400°C. At this temperature the exhaust valves were opened the manner that the evacuated ammonia gas was replaced by ambient air. This last phase stops ions diffusion and decrease temperature down to room one. The yielded figures give the experimental amplitude and phase ( fig.3) variations of the photothermal signal versus depth for samples 1 and 2, which correspond respectively to maintenance durations T 1=24h, T2=30h and T 3=36h. It can be noted that both amplitude and phase increase beneath the sample surface until a certain depth between 100 and 220μm according to the maintenance duration. Both parameters are constant beyond this depth because of the homogeneity of the untreated heart of the sample. Microhardness measurements were also performed on the same samples (fig. 4).
4.c Discussion and analysis We can notice here that the investigation inside nitrured samples is less fluent than in carburized ones. In fact, the prospected effective depth inside nitrured samples doesn’t exceed 80 µm (fig. 5). This feature is explained by the important dimension of nitrogen ion when compared to carbon, and makes the diffusion inside the steel material more and more difficult. Nevertheless, the few experimental points could yield a linear correlation, specially if we gather the points that correspond to the non treated material (depths > 100µm) and replace them by a central pondered one. This is a very relevant result, since we conjectured further correlation under the condition of composition alteration, which is the actual case.
5. Conclusion In conclusion, it was shown that the existence of a first order correlation between thermal diffusivity and Vickers micro-hardness is confirmed an extended to differently structure-altered material. The recent analysis of conjoint mechanical and thermal characteristics variations inside nitrured steel yielded a linear dependence not very different from the already established one inside carburised samples. Our aim is actually to test the same samples under several quenching and annealing treatments, in order to restrain the linear correlation exclusively to structure change cases.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 14. 15. 16. 17. 18 19.
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Figure 1 : Most common photothermal technique disposals scheme .
Figure 2 : Carburized samples: (a) Thermal diffusivity-Hardness profiles inside carburized quenched {Martensite} and annealed {Pearlite} steel . (b) Thermal diffusivity-Hardness correlation inside carburized steel sample.
Figure 3: Photothermal signal amplitude and phase variations versus depth
Figure 4: Microhardness profile inside nitrured steel samples
Thermal Diffusivity (m2/s)
Nitrured samples Diffusivity-Microhardness first-order correlation 0,000015
Sample 1 (Duration of nitruration= 24h) Sample 2 (Duration of nitruration= 30h) Sample 3 (Duration of nitruration= 36h)
0,000010
0,000005
200
300
400
500
600
700
800
900
Microhardness (HV) Figure 5 : Thermal diffusivity-Hardness correlation inside studied nitrured samples.
