WO2008107660A1 - Procédé de soulagement de contrainte résiduelle dans une structure soudée - Google Patents

Procédé de soulagement de contrainte résiduelle dans une structure soudée Download PDF

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Publication number
WO2008107660A1
WO2008107660A1 PCT/GB2008/000721 GB2008000721W WO2008107660A1 WO 2008107660 A1 WO2008107660 A1 WO 2008107660A1 GB 2008000721 W GB2008000721 W GB 2008000721W WO 2008107660 A1 WO2008107660 A1 WO 2008107660A1
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Prior art keywords
heating
stress
region
temperature
welded
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PCT/GB2008/000721
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English (en)
Inventor
Nicholas Mark Bagshaw
Christopher Scott Punshon
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The Welding Institute
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Publication of WO2008107660A1 publication Critical patent/WO2008107660A1/fr

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Classifications

    • C—CHEMISTRY; METALLURGY
    • C21—METALLURGY OF IRON
    • C21D—MODIFYING THE PHYSICAL STRUCTURE OF FERROUS METALS; GENERAL DEVICES FOR HEAT TREATMENT OF FERROUS OR NON-FERROUS METALS OR ALLOYS; MAKING METAL MALLEABLE, e.g. BY DECARBURISATION OR TEMPERING
    • C21D9/00—Heat treatment, e.g. annealing, hardening, quenching or tempering, adapted for particular articles; Furnaces therefor
    • C21D9/50—Heat treatment, e.g. annealing, hardening, quenching or tempering, adapted for particular articles; Furnaces therefor for welded joints
    • C—CHEMISTRY; METALLURGY
    • C21—METALLURGY OF IRON
    • C21D—MODIFYING THE PHYSICAL STRUCTURE OF FERROUS METALS; GENERAL DEVICES FOR HEAT TREATMENT OF FERROUS OR NON-FERROUS METALS OR ALLOYS; MAKING METAL MALLEABLE, e.g. BY DECARBURISATION OR TEMPERING
    • C21D1/00—General methods or devices for heat treatment, e.g. annealing, hardening, quenching or tempering
    • C21D1/34—Methods of heating
    • C21D1/42—Induction heating
    • C—CHEMISTRY; METALLURGY
    • C21—METALLURGY OF IRON
    • C21D—MODIFYING THE PHYSICAL STRUCTURE OF FERROUS METALS; GENERAL DEVICES FOR HEAT TREATMENT OF FERROUS OR NON-FERROUS METALS OR ALLOYS; MAKING METAL MALLEABLE, e.g. BY DECARBURISATION OR TEMPERING
    • C21D11/00—Process control or regulation for heat treatments
    • C—CHEMISTRY; METALLURGY
    • C21—METALLURGY OF IRON
    • C21D—MODIFYING THE PHYSICAL STRUCTURE OF FERROUS METALS; GENERAL DEVICES FOR HEAT TREATMENT OF FERROUS OR NON-FERROUS METALS OR ALLOYS; MAKING METAL MALLEABLE, e.g. BY DECARBURISATION OR TEMPERING
    • C21D6/00—Heat treatment of ferrous alloys
    • C21D6/004—Heat treatment of ferrous alloys containing Cr and Ni
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P10/00—Technologies related to metal processing
    • Y02P10/25—Process efficiency

Definitions

  • the invention relates to methods for relieving residual stress in a welded structure.
  • the welding process in most metals introduces residual stresses in the weld zone.
  • a weld zone is defined as the weld joint and adjacent area surrounding the weld joint wherein the material is thermally affected by the weld procedure and tensile residual stresses are present.
  • Tensile residual stresses render the material more prone to stress corrosion cracking or failure due to external stress influences on the welded part in service. It is therefore common practice to employ post weld thermal stress relief in order to relieve such stresses and thus improve the performance of the welded structure.
  • thermal stress relieving relies on the uniform heating of the welded structure enabling the relaxation of peak stresses. After the stress relief process some residual stress may still be present in the welded structure but at a much lower level and without excessive peaks.
  • induction heating is a non-contact heating method, in which the heat generated from the excited atoms dissipates through the component by conduction.
  • induction heating can provide advantages such as improved uniform heating of the component, reduced cycle time, lower consumables costs, safety, reliability, versatility and ease of use.
  • US-A-4694131 describes an induction heating method for use with a pipe assembly having main and branch types. This addresses the problem of achieving uniform or substantially uniform heating of the structure. In this case, a high-frequency induction heating coil is wound around the joint between the main and branch pipes and then the induction heating stress relief process is carried out. In that process, the weld joint and surrounding regions are subjected to substantially uniform induction heating to a desired temperature thus achieving stress relief.
  • induction heating to achieve stress relief is described in US 6884975.
  • the weld joint and adjacent region is heated using susceptor plates to high temperature of at least 76O 0 C so that once again the material undergoes significant creep and the stress is relaxed.
  • a problem is that the temperatures required to achieve residual stress relief through the use of susceptor plates are high, above the metallurgically significant temperature of the material causing metallurgical changes in the material.
  • a problem with these conventional methods is the need to induction heat to very high temperatures. This is undesirable in certain cases, particularly when relieving stresses in welding structures such as containers which contain hazardous materials such as nuclearwaste. Also local heating can introduce undesirable stresses within the structure.
  • the known methods are not particularly suitable for use with thick section structures (typically greater than 10mm thick) because of the difficulty of achieving uniform heating to the required high temperature. In these cases, typically stress relief is achieved using furnaces and the like.
  • a method of relieving residual stresses in a welded structure having a region of tensile stress adjacent a weld joint and a first region of compressive stress adjacent the region of tensile stress comprising controllably heating the first compressive stress region under working conditions such that tensile stress is induced in the first compressive stress region and corresponding compressive stress is thereby induced in the tensile stress region whereby tensile stress in the tensile stress region is relieved.
  • the inventors realized that one of the problems with the known heating techniques was that they relied on raising the temperature of the structure sufficiently high to cause creep and other metallurgical changes in order to achieve stress relief. They found, surprisingly, that it was possible to achieve stress relief at much lower temperatures by controlling the location of heating making use of the knowledge of the distribution of stress within the welding structure.
  • the region immediately adjacent the weld joint exhibits longitudinal tensile stress while beyond that region is a region of longitudinal compressive stress. Controllable heating causes tensile stress to be induced into the heated region.
  • tensile stress will be induced in that region and cause balancing compressive stresses to be induced in the region of tensile stress adjacent the weld joint.
  • This induction of compressive stress into the tensile stress region will relieve stresses in the tensile stress region.
  • the working conditions must be chosen carefully so that the amount of tensile stress induced into the compressive stress region is not too high but this can be done by careful modelling.
  • the technique described herein is not a thermally driven recovery stress relief method, wherein there is diffusion of vacancies, but rather a method of redistributing stress by means of thermally inducted stress local to the weld joint.
  • Induction heating is an important example of a method of achieving controllable heating because it is possible to control accurately the heating location and temperature distribution. Methods such as flame heating are uncontrolled and not suitable.
  • power sources such as electron beams.
  • the advantage of these is that the same equipment, e.g. an electron beam system, can be used to carry out a weld and to achieve stress relief.
  • controllable heating can be carried out from one side of the structure.
  • thick section it may be necessary to heat on both sides of the workpiece or structure.
  • the technique shows a significant reduction and in some cases an elimination of residual tensile stresses in the weld zone.
  • the technique is a thermal postweld stress relief method with no limitation on the type of metal or metals the workpiece comprises.
  • the welded structure will be subject to heat exposure resulting in through thickness heating in a confined area.
  • the preferred technique utilises induction-heating coils whereby the area exposed to heating is dictated by the position and shape of the induction coil(s).
  • the technique uses a temperature below the metallurgically significant temperature of the material to be treated (where above this temperature the material will undergo appreciable metallurgical changes). For example, for metals such as Ni alloys and for steels, the maximum tolerable temperature is approximately 400°C although for some steels this can be higher. Also, as less area needs to be heated compared to traditional methods for thermal stress relief, the energy savings through use of the technique are significant. Thus the technique described herein relies almost solely on stress management avoiding metallurgical changes in the work-piece(s). In general temperatures up to 500 0 C are envisaged, and depending upon circumstances these may lie in the ranges 100-200°, 200-300°C, 300-400 ⁇ C, and 400- 500°C.
  • the magnetic field preferably alternates at a low frequency, typically 50Hz-IOMHz, for example substantially 9OkHz.
  • mst metalgically significant temperature
  • the alloy will begin to soften above its mst.
  • the mst represents an embrittlement temperature, grain growth temperature, or the temperature at which precipitation begins to occur.
  • the positions of the tensile stress and compressive stress regions are determined.
  • this can be done by reference to existing data (such as experimental results or previously published data) or by using numerical methods such as finite element (FE) modelling.
  • FE modelling is preferred as it is fast and versatile.
  • the appropriate working conditions can be determined through experiment or preferably by further modelling the controllable heating process and reviewing the predicted stress distribution. If the predicted stress distribution is not satisfactory then the modelling process is repeated until the appropriate parameters have been defined. From these parameters, it is a relatively straightforward step to define the form of the inductive heating coils and induction parameters (in the case of induction heating).
  • the welded structure may be made from components of the same material or different material components and may have a consistent or varied thickness across its profile.
  • the penetration depth of the heating will determine if through thickness or near surface stress relief is attained.
  • the degree of stress relief required is application specific thus the penetration depth required will be known or can be determined.
  • the method was noted to be particularly beneficial for the residual stress relief of single pass welds, e.g. electron beam, laser and plasma keyhole, where the residual stress profile of such welds have the highest residual stress located sub-surface in the weld itself and predominately in the mid-thickness of the weld.
  • the technique is particularly advantageous for thick plates, large structures and complex structures, offering a more practical post-weld stress relief method than those commonly employed.
  • the technique is particularly suited to the stress relief of thick workpieces, 10mm and over, where traditional stress relief techniques tend to be cumbersome and/or time consuming. Examples of suitable materials on which this method can be performed include nickel, aluminium alloy, steel, copper or any other metal and it's alloys.
  • Figures 1A and 1 B are a plan and cross-section respectively illustrating schematically the arrangement of induction coils and welded structure or workpiece according to a first example
  • Figure 2 shows an arrangement of induction coils aligned either side of the weld joint on the upper face of the workpiece only;
  • Figure 3 illustrates the longitudinal stress distribution (section view) of electron beam welded Alloy 22 (one side only);
  • Figure 4 is a representation of an induction-heating coil
  • Figure 5 is a graph of FE prediction and measurement of the residual stress profiles in the Alloy 22 RPEB welded work-piece, comparing the as welded stress state with the post-weld induction heating stress state on top face of plate;
  • Figure 6 illustrates a longitudinal stress distribution (section view) of reduced pressure electron beam welded C-Mn Steel (one side only);
  • Figure 7 is a graph of FE prediction and measurement of the residual stress profiles in the C-Mn Steel RPEB welded workpiece comparing the as welded stress state with the post-weld induction heating (IH) stress state on top face of plate;
  • Figure 8 illustrates a longitudinal stress distribution (section view) of gas tungsten arc welded Alloy 22 (one side only);
  • Figure 9 is a graph of FE prediction and measurement of the residual stress profiles in the Alloy 22 GTAW welded workpiece comparing the as welded stress state with the post-weld induction heating (IH) stress state on top face of plate;
  • Figure 10 illustrates a method for deploying an electron beam to locally heat the surface regions either side of a weld (units in 0 C);
  • Figure 11 illustrates a finite element (FE) prediction of a residual stress distribution in welding Alloy 22 plate, showing as-welded and post-weld stress relief using a reflected electron beam;
  • Figure 12 illustrates an FE prediction of surface residual stresses in welded Alloy
  • Figure 13 is an FE prediction of temperature in a thin test specimen (2 millimetre thick stainless steel 304L);
  • Figure 14 is a schematic illustration of a thin plate test specimen that was used to measure the temperature distribution of moving heat sources;
  • Figures 15a - 15c illustrate FE prediction and thermocouple measurement of temperature on a thin plate test specimen.
  • FIGS 1A and 1B illustrate a welded plate structure or workpiece 1 having a weld joint 2.
  • the welded structure 1 exhibits regions of tensile stress 3 adjacent regions of compressive stress 4. These are symmetrically arranged about the weld joint 2.
  • the induction coils 7,8 are located coaxially above and below the workpiece 1 adjacent the tensile stress region 3B so as to induction heat the compressive stress region 4B. Again, no magnetic field is generated in the tensile stress region 3B. Relative movement between the coils 5-8 and the welded structure 1 is then caused so that the induction coils traverse along paths parallel with the weld joint
  • each coil may extend along the full length of the weld joint 2 so that no relative movement is required.
  • FIG. 1 shows an induction coil arrangement where the coils are aligned either side of the weld joint on the upper face of the workpiece. For complex joints in inaccessible areas there may be only the opportunity to run an induction coil on one side of the weld joint; this will render residual stress relief but only on the side of the workpiece treated.
  • the stress profile of the welded workpiece 1 is determined. This may be from prior work, typical stress distribution tables or other. From this the approximate positioning of the centre of the induction coils 5-8 can be determined, being the region of compressive stress 4A,4B near the transition point of the tensile to compressive stresses.
  • the material or material type(s) and thickness(es) are known for the welded component 1. It is also known what metallurgically significant temperature is applicable for the material(s) type(s). An induction heating temperature below this will be used for the stress relief method.
  • the induction heating coil power supply frequency and shape of the coil cause different stress profiles. Assuming a suitable heated volume in the near surface region, where the heat is dissipated through the workpiece by conduction heating effects, simulates the heating effect of the induction coils (suppliers of induction equipment will have data on volumetric size of the heated area and the conduction effects achieved). Alternatively one can assume uniform through thickness heating of the workpiece wherein the target predicted tensile residual stress reduction is exceeded and these parameters are used in practice. The combinations of those parameters that achieve an adequate reduction in tensile stress at the weld are deemed suitable for practical application.
  • the requirements of the stress relief method are established: the size of power supply (not shown), the power input and frequency, the number and location of the induction-heating coils on the welded workpiece; and a practical translation speed that achieves localised through-thickness heating of the welded workpiece.
  • Models were run with the coils positioned on the top face of the welded workpiece only and with the coils positioned on the top and bottom faces of the welded workpiece.
  • the temperature of the coil as seen by the workpiece
  • different residual stress plots could be generated.
  • the induction coils were positioned on the top face of workpiece either side of the weld centreline, and traversed along the plate at 5mm/s (300mm/min).
  • the maximum temperature in the model workpiece was approximately 400°C.
  • the parameters established by the FE model were then applied to the RPEB welded workpiece.
  • induction heating on the top face of the welded workpiece generated sufficient reduction in tensile stress
  • two coils were positioned 45mm from the weld centreline.
  • the induction coils were translated at a speed of approximately 5mm/s (300mm/min).
  • Through thickness heating was affected by the induction coils, where 18kW of power was consumed in order to generate sufficient heating through the thickness of the workpiece.
  • the coils were operated with a power supply frequency of 9OkHz, which generated a maximum temperature between 300- 400 0 C.
  • a stress graph is plotted in Figure 5, showing the results of FE prediction and measurements of residual stresses on the top surface of the plate.
  • the experimental residual stress measurements were taken using the hole drilling method. It can be seen from the stress profiles generated that when the stress relief method is adopted, the tensile stress at the weld joint of approximately 390MPa (yield magnitude) drops to 100MPa (25% yield strength). Thus a significant reduction in tensile stresses in the weld zone is achieved. Between 5 and 20mm from the weld centreline, the residual stresses were less than 50MPa for both FE prediction and experimental measurement.
  • Example 2 Reduced pressure electron beam (RPEB) welded C-Mn Steel
  • the induction coils were positioned on the top face of workpiece either side of the weld centreline, and traversed along the plate at 5mm/s (300mm/min). The maximum temperature in the model work piece was approximately 500 0 C. The parameters established by the FE model were then applied to the RPEB welded workpiece.
  • induction heating As the use of induction heating on the top face of the welded workpiece generated sufficient reduction in tensile stress, two coils were positioned 45mm from the weld centreline. The induction coils were translated at a speed of approximately 5mm/s (300mm/min). Through thickness heating was affected by the induction coils, where 18kW of power was consumed in order to generate sufficient heating through the thickness of the workpiece. The coils were operated with a power supply frequency of 9OkHz, which generated a maximum temperature between 400- 500 0 C.
  • a stress graph is plotted in Figure 7, showing the results of FE prediction and measurements of residual stresses on the top surface of the plate.
  • the experimental residual stress measurements were taken using the hole drilling method. It can be seen from the stress profiles generated that when the stress relief method is adopted, the tensile stress at the weld joint of approximately 400MPa ( ⁇ yield magnitude) drops to - 100MPa (compressive stress). Thus an elimination of tensile stresses in the weld zone was achieved.
  • GTAW Gas Tungsten Arc Welded
  • the metallurgically significant temperature of Alloy 22 is approximately 400 0 C hence temperatures on or below this value were investigated.
  • the induction-heating coils were pre-existing coils having a power supply frequency of 90Hz and each coil having a diameter of 50mm, Figure 4.
  • the induction coils were translated at a speed of approximately 5mm/s (300mm/min). Through thickness heating was affected by the induction coils, where 18kW of power was consumed in order to generate sufficient heating through the thickness of the workpiece.
  • the coils were operated with a power supply frequency of 9OkHz, which generated a maximum temperature between 200-
  • a stress graph is plotted in Figure 9, showing the results of FE prediction and measurements of residual stresses on the top surface of the plate.
  • the experimental residual stress measurements were taken using the hole drilling method. It can be seen from the stress profiles generated that when the stress relief method is adopted, the tensile stress at the weld joint of approximately 400MPa ( ⁇ yield magnitude) drops to 150MPa (40% yield strength). Thus a significant reduction in tensile stresses in the weld zone is achieved.
  • thermal stress relief is predominantly driven by recovery which is the dominant mechanism in secondary creep.
  • recovery is the dominant mechanism in secondary creep.
  • the increased strain energy stored in the metal due to deformation, together with the high temperature, provides a driving force for the process of recovery.
  • n Q is the number of lattice sites and Q ⁇ is the activation energy for vacancy creation and movement, (or the activation energy for self-diffusion).
  • HP T(20+log 10 t) x10- 3 This indicates that heating ferritic steel of 25mm thickness to 62O 0 C for 1 hr, which is a well established post weld heat treatment for stress relief of welded structures in C-Mn steel, causes the same degree of stress relaxation as heating the same material to 500 0 C for ⁇ 1500hrs. Thus at the temperatures and short times proposed for residual stress management in the patent application (i.e ⁇ 400 ° C for a short time) very little in the way of metallurgical change or stress relaxation would normally be expected to occur.
  • a FE model was created of an Alloy 22 weld to investigate the effectiveness of electron beam stress relief.
  • the model simulated one side of the weld by using symmetry boundary conditions, as shown in Figure 10 which also shows the heat source assumed to be generated by the deflected electron beam.
  • the model represented two moving heat sources (50x50mm) either side of the weld centreline.
  • the centre of the heat sources were 45mm from the weld centreline.
  • the maximum temperature of the moving heat sources were approximately 25O 0 C.
  • the residual stresses in the as-welded and post weld stress relief states were predicted and are contour plotted in Figure 11 , showing sectioned views of the plate.
  • the longitudinal tensile stress generated from welding, residing predominately in the weld zone region, is balanced in equilibrium with compressive stresses adjacent.
  • the deflected EB produced low tensile stress in the region of heating, which were balanced by a comparable compressive stress adjacent in the weld region.
  • This compressive stress component significantly reduced the initial weld tensile stress.
  • a line plot, given in Figure 12, shows a 50% reduction of longitudinal tensile residual stress at the weld centreline.
  • the thin plate allowed the heat to conduct through the thickness quickly, and hence the temperature distribution on the bottom surface was similar to that on the top.
  • the size and intensity of the heated regions could therefore be measured using thermocouples located on the bottom surface (opposite side to the heated surface).
  • the heating parameters of the Alloy 22 modelling work were used as guidance for the power input for the calibration test.
  • a model using 2mm thick stainless steel 304L was carried out to predict the temperature distribution using these heating parameters.
  • the results of the model are plotted in Figure 13, producing a maximum temperature of 585°C on the bottom surface.
  • the beam deflection system was then calibrated by comparing the temperatures from the thermocouples with the predicted temperature distribution.
  • FIG 14 gives a schematic illustration of the beam deflection calibration test, showing the location of the thermocouples.
  • the electron beam was deflected either side of the weld at a frequency of 30Hz producing 2000 points per square of heating, and was traversed along the plate at 300mm/min.
  • the test was performed twice for different beam powers.
  • the voltage potential across the gun was 15OkV.
  • a current of 8mA was initially used in the first run, followed by a current of 14mA, producing power inputs of 1.2 and 2.1 kW respectively.
  • Figure 15 shows transient temperature plots of the FE prediction and the thermocouple measurements. The maximum temperatures were recorded at thermocouples T3 and T6, which were located at the centre of the heated regions.
  • thermocouple T5 measured 225 and 315 0 C for beam currents of 8 and 14mA respectively, see Figure 15(b).
  • the target temperature estimated by the model, was 320 0 C.
  • the temperatures were relatively higher at thermocouple T5 than at T3 and T6.
  • the temperatures were relatively lower at thermocouple T1 that T3 or T6, see Figure 15 (c), which indicated that the heat sources were slightly outside the designated heated region being closer to the weld centreline. Nevertheless, the experimental results showed that the beam deflection system was producing similar trends to the FE prediction.

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Abstract

L'invention concerne un procédé de soulagement de contraintes résiduelles dans une structure soudée (1) ayant une région de contrainte de traction (3) adjacente à un joint de soudure (2) et une première région de contrainte de compression (4) adjacente à la région de contrainte de traction. Le procédé comprend le chauffage de façon contrôlable, typiquement le chauffage par induction, de la première région de contrainte de compression (4) dans les conditions de travail telles que la contrainte de traction est induite dans la première région de contrainte de compression et une contrainte de compression correspondante est ainsi induite dans la région de contrainte de traction (3), de telle sorte que la contrainte de traction dans la région de contrainte de traction est soulagée.
PCT/GB2008/000721 2007-03-02 2008-02-29 Procédé de soulagement de contrainte résiduelle dans une structure soudée WO2008107660A1 (fr)

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GB0704118.9 2007-03-02
GBGB0704118.9A GB0704118D0 (en) 2007-03-02 2007-03-02 Method of relieving residual stress in a welded structure

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CN101713021B (zh) * 2009-09-23 2012-03-28 清华大学 一种降低铁磁性金属材料残余应力的方法
EP2492042A1 (fr) * 2009-12-04 2012-08-29 Nippon Steel Corporation Joint soudé bord à bord d'une structure soudée et procédé de fabrication de ce joint
CN104722978A (zh) * 2015-03-30 2015-06-24 广东省工业技术研究院(广州有色金属研究院) 一种便携式焊接变形控制设备及其变形处理方法
US20180094333A1 (en) * 2012-11-16 2018-04-05 Nippon Steel & Sumitomo Metal Corporation Stress-relief heat treatment apparatus
CN110484709A (zh) * 2019-08-06 2019-11-22 中国船舶重工集团公司第七二五研究所 一种消除核反应堆堆内密封筒焊接应力的方法
CN110541067A (zh) * 2019-09-06 2019-12-06 鞍钢股份有限公司 防止高碳当量真空特厚复合坯焊缝开裂的焊后加热工艺
US10508316B2 (en) * 2017-03-31 2019-12-17 General Electric Company Method and fixture for counteracting tensile stress
CN110895634A (zh) * 2018-09-11 2020-03-20 南京航空航天大学 一种面向精确变形控制的2.5mm厚度铝锂合金T型接头焊接结构集成模拟方法
CN112149330A (zh) * 2020-09-24 2020-12-29 河海大学常州校区 一种风电塔筒油封平台焊接残余应力预测、焊接工艺优化方法
CN112935256A (zh) * 2021-01-26 2021-06-11 四川大学 基于脉冲磁场的非铁磁性粉末烧结金属零部件的改性方法
WO2021184537A1 (fr) * 2020-03-20 2021-09-23 中国石油大学(华东) Procédé de traitement thermique local de régulation de contrainte résiduelle par chauffages primaire et auxiliaire

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