Thermo-Mechanical Response of an Automotive Power Module Heat Sink under Combined Thermal and Power Cycling

Power electronics modules are increasingly used in the automotive and industrial sectors, where reliability under harsh operating conditions is a fundamental design requirement [1], [2], [3]. In these systems, heat sinks play a key role in ensuring effective thermal management, contributing to stable performance and component durability. However, exposure to repeated thermal cycling and variable power loads could generate complex stress states, resulting in deformations that, over time, can compromise the integrity of the system. Additionally, accelerated thermal and power cycling are widely recognized as critical methodologies for evaluating long-term degradation and thermo-mechanical reliability in automotive and industrial power modules [4].

Thermal cycling and power cycling tests are commonly used to simulate real-world operating conditions of power modules, as they reproduce both ambient temperature variations and internal heating due to electrical stresses. For example, early experimental investigations on fast power cycling of IGBT modules demonstrated the relevance of cyclic thermo-mechanical loading for reliability assessment in traction and automotive applications [5]. These studies established the basis for accelerated endurance testing procedures currently adopted in qualification protocols. In general, thermo-mechanical degradation mechanisms in power modules have been extensively investigated in the literature, particularly with reference to fatigue phenomena induced by cyclic thermal loading and material mismatch within multilayer assemblies. Ciappa [6] identified the dominant failure mechanisms affecting modern power modules, highlighting the critical role of thermo-mechanical stresses generated during repetitive thermal excursions.

In this context, the thermo-mechanical behavior of heat sinks is particularly relevant. The induced deformations can affect the contact between the various components, the efficiency of heat exchange, and, more generally, the overall reliability of the device.

Experimental strain measurement is typically performed using resistive strain gauges, which allow highly precise detection of local surface deformations. However, measurement accuracy can be affected by several factors, including thermal compensation, sensor placement, and test of environmental conditions. Therefore, the design of proper measurement system and accurate interpretation of acquired data are essential.

State-of-the-art research already outlines the essential building blocks of a rigorous thermo-mechanical study on automotive power modules. Advanced numerical frameworks now combine finite-element temperature–stress fields with data-driven life-prediction tools, as demonstrated by Lee et al. [7]. Their workflow directly informed the pre-test simulations used here. Robust strain-gauge practice is equally well-established: Wang et al. [8] reviewed high-temperature grid alloys while bridging layouts and compensation schemes. Besides, Avery [9] provided a validated protocol including bonding, Wheatstone wiring, and dual zeroing, to mirror the “double-zero + SG0” procedure in the current study. On the loading side, DeVoto [10] consolidated failure modes and standardised power thermal cycle endurance (PTCE) profiles for automotive qualification, and McVicker et al. [11] highlighted how heat-sink clamping could amplify solder-joint strain, thus underscoring the need to track bolt preload in our set-up. Real-time strain acquisition under combined current and temperature swings has already been proven on press-pack insulated-gate bipolar transistors (IGBTs) by Ren et al. [12], to confirm the feasibility of our PTCE monitoring strategy. Finally, system-level reviews by Yang et al. [13] positioned the present dual-plate heat sink within current Si/SiC packaging trends, while Van der Broeck [14] detailed best-practice routines for correlating finite element method (FEM) thermal fields with strain-gauge data, i.e., the routines adopted here to benchmark numerical and experimental curves.

Previous studies focused primarily on junction-to-case temperatures or on global warpage, while the local strain field within automotive-scale heat sinks remains poorly documented. Moreover, the influence of assembly preload introduced by screw tightening on the subsequent thermo-mechanical response is rarely quantified.

The present work addressed these gaps by measuring, with ten resistive strain gauges, the in-service deformation of a dual-plate heat sink belonging to an industrial Power Integrated Module (PIM). After a double zeroing procedure that isolates mechanical preload from thermal effects, the instrumented device is subject to (i) climatic-chamber cycling between -40 $^\circ\text{C}$ and +75 $^\circ\text{C}$; and (ii) realistic PTCE sequences featuring twelve 0.5 s current surges per 30-min cycle. The study (i) quantified strain amplitudes; (ii) evaluated the impact of screw tightening; and (iii) assessed compensation strategies for sub-zero testing, hence providing design and metrology guidance for next-generation automotive PIMs.

In doing so, the work dealt with the limited availability of experimental data on local strain fields in automotive-scale heat sinks under combined thermal and power cycling conditions. Its novelty lied in the integrated experimental approach, which combined: (i) a controlled separation of assembly preload effects through a double zeroing procedure; (ii) distributed strain measurements using multiple strain gauges, including redundant and compensation channels; and (iii) monitoring under both climatic chamber cycling and service-like PTCE conditions. These elements enabled a more detailed interpretation of the thermo-mechanical behaviour of the heat sink and provided practical guidance for both design of experimental setup and data interpretation in similar applications.

The overall objective of the present work is to investigate the behaviour of a power module operating under critical service conditions. The experimental validation phase focused on the design and implementation of a test setup aimed at measuring, by means of strain gauges, the deformation of a heat sink induced by thermal loading during the test cycle. These displacements were intended as a first-order approximation, to provide a useful order-of-magnitude indication of the structural response, based on a simplified analytical interpretation of the system.

Specifically, the validation included the following steps:

1. Device operating principle analysis

2. Review of the structural layout and identification of expected issues

3. Identification of critical areas

4. Measurement issues and selection of instrumentation

5. Definition of test plan

6. Installation of strain gauge

7. Data acquisition wiring and zero calibration

8. Deformation acquisition before and after assembly

9. Deformation acquisition during climatic chamber thermal cycles

10. Deformation acquisition during combined thermal and power cycling

11. Result analysis and interpretation

Wherever possible, test protocols were aligned with internationally recognised standards to ensure repeatability and traceability. Bonded resistance gauges were installed, calibrated, and zero-balanced in accordance with ASTM E251 [15]; extensometer accuracy was verified to ISO 9513 class 0.5 before each test series [16]. Temperature-cycling profiles (-40 $^\circ\text{C}$ $\leftrightarrow$ +75 $^\circ\text{C}$, 10-min dwells) followed IEC 60068-2-14, Test Nb [17], and the semiconductor-specific requirements of JEDEC JESD22-A104G [18]. Power-cycling sequences (12 current surges per 30 minute, $\Delta T_{j}$ $\approx$ 45 $^\circ\text{C}$) were derived from the automotive guideline ECPE AQG 324 [19] and cross-checked against the stress-test limits of ECPE ST-2010 and JEDEC JESD22-B111A [20], [21]. Climatic-load severity (humidity $<$ 10% RH, sub-zero hold) respected ISO 16750-4 class III for in-cabin electronics [22].

The system under investigation was a largely commercial PIM for automotive applications, featuring a multilayer structure integrated into a thermal dissipation system (Figure 1).

From a construction standpoint, the system was composed of:

a) A heat sink made of aluminium alloy, with a relatively flat geometry and longitudinal development;

b) A central active plate, on which the power electronic components (chips) are mounted;

c) An electrical and thermal interconnection system between the chips and the heat sink;

d) A further heat sink;

e) A plastic structural frame, which both integrates and holds the assembly; and

f) A fastening system using screws, distributed along the length of the device.

The PIM operated as a power electronic module in which heat generated by active devices was transferred to one of the two metallic heat sinks and then dissipated to the environment. The non-uniform distribution of thermal loads, combined with discrete mechanical constraints and material heterogeneity, induced thermo-mechanical deformation of the heat sink during operation.

The cross-sectional view (Figure 2) shows that the active devices are arranged along a central line and thermally coupled to the heat sinks through dedicated interfaces. Each heat sink represents the primary element responsible for heat dissipation toward the external environment. The system exhibits a configuration that is approximately symmetric with respect to the median plane, with lateral constraints and localized fastening points. The surrounding plastic frame mainly acts as a mechanical support, without providing a continuous rigid constraint to the structure.

With overall dimensions of 180 × 80 mm, the system is characterized by the presence of fastening holes distributed along the perimeter, thus ensuring mechanical coupling with the assembly. The spacing between load application points and constraint locations plays a key role in the deformation analysis of the system.

In short, the device can be idealized as a heat-dissipating plate subject to localized thermal loads and constrained by discrete fastening points, such as screws. Furthermore, the interaction between materials with different stiffness, namely the metallic heat sink and the surrounding plastic frame, contributes to the overall mechanical response of the system. This configuration typically results in out-of-plane deformations, localized strain gradients, and coupled thermo-mechanical effects.

Multiple zones of localized heat dissipation can be identified in the heat sink, roughly corresponding to the position of the power devices. Therefore, the thermal loads are not uniformly distributed, with peak values reaching up to approximately 200 W in the main regions and around 105 W in secondary areas (Figure 3).

For the investigation of the two heat sink deformations, the following instrumentation was employed:

• A Vishay P3500 analogic data acquisition system based on a Wheatstone bridge configuration, featuring voltage output and equipped with a module including 10 input analogic channels and 1 output channel, with individual channel balancing capability.

• N. 10 pre-wired resistive strain gauges (SGs) with a nominal resistance of 120 $\Omega$, applied using a bonding adhesive suitable for the expected thermal range [-40 $^\circ\text{C}$ - 100 $^\circ\text{C}$] and with special attention to avoid interference with the sealing area (Figure 4), follow a “8 + 1 + 1” layout. Their installation and calibration have considered the requirements of ASTM E251 for bonded metallic strain gauges [15].

Specifically, eight strain gauges were bonded directly onto the aluminium heat-sink plates, four on the upper sink and four on the lower, to capture the local thermo-mechanical strains in the hottest zones. Their locations were defined to capture the most representative deformation fields, based on a preliminary finite element analysis. Figure 5 shows the positioning of the eight internal SGs on the two heat sinks and defines their labelling. In the gauge code, the suffix “R” (for redundant) marks the second element of each very-close pair installed on the same hotspot as the twin reading allows us to check repeatability and to spot any local debonding or wiring faults. On the other hand, the suffix “C” (for compensation) designates the gauge reserved for thermal compensation. This sensor is either left free or bonded to an inert reference coupon, so it is not mechanically loaded; its signal is subtracted from the active gauges to remove electronic drift and purely thermal output, leaving only the true mechanical strain.

A 9$^{\text {th}}$ gauge (SG5) was glued to the metal-interconnection tray that bridges the two plates, to provide a measure of the overall bending of the stack. The 10$^{\text {th}}$ gauge (SG0) was left unbonded and merely followed the chamber temperature, thus serving as a free reference channel to subtract electronic drift and pure thermal output from the other sensors.

A preliminary pre-test was carried out to verify the correct functioning of the measurement system under purely mechanical loading conditions. In this phase, the zero of the measurement system was first established to remove initial offsets and define the reference baseline for all subsequent strain measurements (Figure 6). Then, the module was progressively assembled. Instrumented strain signals were recorded throughout the main assembly stages, namely initial calibration, PIM tightening, co-molded screw tightening, spring installation, housing tightening, PIM tightening on the test fixture, and PIM removal from the test fixture.

The purpose of this measurement was not to evaluate the performance of the device, but rather to confirm that the strain gauges, once bonded and connected to the acquisition chain, were able to properly detect the strain induced by the assembly preload. The tightening sequence was performed using M5 × 8 screws, corresponding to a calculated stress of -21.24 MPa, while the average strain measured after tightening was approximately -177 $\mu$m·m$^{-1}$. Since the device was not electrically powered during this phase, the recorded strain response could be entirely attributed to the mechanical effects associated with fastening and assembly. The strain values measured during this phase were subsequently used to re-balance the measurement system, so as to exclude the effects associated with assembly and fastening from the subsequent analysis of the system behavior.

This pre-test therefore provided an initial verification of the measurement system, while also establishing a useful mechanical baseline for the interpretation of the subsequent tests performed under thermal cycling and operating conditions. The zero-balance steps were complied with ISO 9513 class 0.5 recommendations for extensometer accuracy and verification [16].

This dual zeroing/balancing procedure defined precise reference conditions to:

1. Eliminate initial offsets, arising from bonding residual stresses, wiring imperfections, Wheatstone bridge imbalances, and electronic drift;

2. Ensure comparability of measurement by setting a common zero reference for all gauges;

3. Define the initial unloaded state of the system, so that subsequent measurements could reflect applied loads only;

4. Separate the different contributions, distinguishing among (a) mechanical effects due to tightening, (b) thermal effects, and (c) combined thermo-mechanical effects.

The second experimental phase was carried out in a controlled climatic chamber environment to assess the stability and reliability of measures under thermal loading conditions. In this stage, the instrumented module was exposed to thermal cycles within the temperature range of -40 $^\circ\text{C}$ to 75 $^\circ\text{C}$, followed by a return to the room temperature of 22 $^\circ\text{C}$, in control of humidity and without applying electrical power to the device. This profile mirrored IEC 60068-2-14, Test Nb, and severity 2, which specified the adopted thermal excursion with 10-min dwells at each extreme [17]. Moreover, the purpose of this test was not to reproduce the actual operating condition of the power module, but rather to verify the behaviour of the measurement system under severe thermal excursions, with particular attention to signal stability, repeatability, and sensitivity to temperature variations. Cycle count, ramp rate ($\leq$ 5K min$^{-1}$), and soak times were aligned with the guidance of JEDEC JESD22-A104G for semiconductor devices [18].

The strain signals were continuously monitored during the heating and cooling phases to detect any possible drift, anomalous response, or inconsistency related to the thermal environment. This test also made it possible to evaluate the thermal stabilization time of the system and to identify possible limitations associated with temperature compensation, especially at sub-zero conditions. For this reason, the heating ramp was extended by including a return to room temperature. Therefore, the climatic chamber tests represented an intermediate validation step between the preliminary mechanical pre-test and the subsequent thermo-mechanical tests performed under actual operating conditions.

The instrumented PIM was tested to evaluate its thermo-mechanical response during actual service-like loading. The tests were characterized by combined thermal and power cycling in PTCE. Each power cycle had a duration of 30 min, with relatively fast dynamics, and consisted of 12 current peaks of 0.5 s each, as derived from European Center for Power Electronics (ECPE) AQG 324 requirements for automotive power modules [19]. Humidity was kept below 10% RH, in accordance with ISO 16750-4 climatic-load class III for in-cabin electronics [22].

Unlike previous tests, the device was activated so that the heat generated by the power components contributed directly to the thermal loading of the assembly. The objective of this stage was to monitor the deformation of the heat sinks under combined thermal and operational effects, thus reproducing more realistically the conditions experienced by the module during service.

The acquisition system continuously recorded the strain signals throughout the test, to allow evolution of deformation to be followed during different phases of the cycle. Due to dynamic nature of the loading, the recorded data were subsequently processed to reduce signal oscillations and facilitate interpretation of the main strain trends. This experimental phase made it possible to assess the structural response of the module under realistic thermo-mechanical conditions and to compare it with the baseline strain state previously identified during assembly and thermal pre-testing.

The strain signals were continuously acquired to monitor the mechanical response of the instrumented PIM under different loading conditions. Particular attention was devoted to the comparison between the strain levels measured during assembly, thermal exposure, and actual operating cycles, so as to distinguish the contribution of each stage to the overall deformation state of the module. In the tests performed under operating conditions, the strain signals exhibited oscillations associated with the cyclic nature of the applied loads and with the rapid thermal transients generated during power activation. For this reason, the raw data were post-processed to improve readability and facilitate interpretation of the underlying deformation trends. A moving average filter was applied to reduce high-frequency fluctuations and highlight main evolution of the strain response during the test cycles. The processed signals were analysed by considering both their absolute values and their variation with respect to the initial reference condition, thus allowing identification of the most significant deformation stages and comparison of the behaviour of the two heat sinks throughout the experimental campaign.

A simplified three-dimensional finite element (FE) model of the assembly was initially implemented using linear elastic material assumptions. The aluminium heat sink was modelled with isotropic properties (Young’s modulus E $\approx$ 70 GPa, Poisson’s ratio v $\approx$ 0.33, coefficient of thermal expansion $\alpha$ $\approx$ 23 × 10$^{-6}$ K$^{-1}$), while the surrounding structural elements were represented using equivalent stiffness properties to account for their mechanical interaction without explicitly modelling all geometric details.

Thermal loading was introduced as a non-uniform heat flux distribution applied to the regions corresponding to the active devices, with peak values consistent with the estimated power dissipation, up to 200 W in primary zones and 105 W in secondary regions (Figure 3). Convective boundary conditions were imposed on the external surfaces to simulate heat exchange with the environment, assuming a uniform heat transfer coefficient representative of natural/forced convection conditions. A steady-state thermal field was first obtained and subsequently mapped onto the structural model to evaluate the induced deformation.

The mechanical boundary conditions were defined to reproduce the effect of the fastening system. The screw locations were modelled as locally constrained regions, restricting out-of-plane displacements while allowing limited in-plane expansion, thus approximating the clamping action without explicitly modelling bolt preload. This approach helps capture the main constraint effect, while maintaining model simplicity.

The mesh consisted of quadratic tetrahedral elements with local refinement in the regions of highest thermal gradients and around the fastening points, to ensure an adequate resolution of strain gradients while limiting computational cost. The analysis was not intended as a full predictive simulation of the complete modular behaviour, but rather as a support tool for interpreting the expected thermo-mechanical response of the heat sink and guiding the experimental setup.

The results highlighted a non-uniform distribution of deformation, with peak values localized in correspondence with the main heat-generating regions, consistently with the imposed thermal load distribution. In particular, the central areas of the plate exhibited the highest deformation levels, while the peripheral regions, especially near the fastening points, showed significantly lower values due to the constraining effect of the boundary conditions (Figure 7 and Figure 8).

The contour maps clearly indicate a smooth gradient of deformation from the high-load zones toward the edges, thus confirming the dominant role of thermal expansion combined with variations of localized stiffness. The section view further emphasizes the out-of-plane deformation of the heat sink, in order to reveal a global bending behaviour induced by the asymmetric thermal field and the interaction with the supporting structure. The effect is particularly evident in the MIT–heat sink assembly, where the coupling between components leads to a redistribution of stresses and deformation along the thickness (Figure 8).

Overall, the numerical results highlighted that the deformation pattern was primarily governed by the spatial distribution of thermal loads and the positioning of the constraints, hence providing a consistent reference for the interpretation of the experimental strain measurements.

On this basis, the FE map also guided a more informed placement of the strain gauges. Rather than keeping the sensors near the heat-sink edges as an option that would have limited their temperature exposure, the analysis recommended locating them along the mid-span of the shorter dimension and arranging each pair in a symmetrical fashion with respect to the longitudinal axis. In this way, the gauges intercepted the highest strain gradients while remaining evenly distributed, thus maximizing both sensitivity and comparability across the plates.

During the tightening test, the integrated module was assembled progressively while the strain signals were continuously monitored throughout the different tightening and mounting stages (Figure 9).

Specifically, the following phases can be distinguished:

A. Initial calibration

B. PIM tightening

C. Co-molded screw tightening

D. Spring installation

E. Housing tightening

F. PIM tightening on the test fixture

G. PIM removal from the test fixture

The results of the tightening test revealed that all strain gauges responded promptly and coherently to the assembly preload. As shown in Figure 10, the signals moved from the initial zeroed condition toward negative strain values immediately after the first tightening operation, indicating a compressive state induced by bolt fastening. This behaviour was fully consistent with the expected mechanical effect of clamping and confirmed that the strain gauges, bonding procedure, and acquisition chain were all functioning correctly. The recorded values were quantitatively plausible, generally ranging from about -120 to -250 $\mu$m/m depending on the measuring point, with an average post-tightening strain of approximately -177 $\mu$m/m under the considered assembly condition. In the upper heat sink, the strain levels became rapidly stable after the initial tightening, while only minor variations were observed during the following assembly stages. A similar trend was found for the lower heat sink though with slightly higher compressive values at some points and a more pronounced response in one gauge, thus suggesting a realistic non-uniform distribution of the fastening load across the structure. No erratic or physically inconsistent signals were observed in either heat sink. Overall, the tightening test confirmed the reliability of the measurement system and demonstrated that the initial assembly process introduced a measurable and non-negligible compressive strain field, which should be regarded as the mechanical baseline for the interpretation of the subsequent thermal and thermo-mechanical tests.

The measurements performed during the thermal cycling tests in the thermal chamber highlighted a clear and repeatable thermo-mechanical response of the heat sink. The observed correlation between temperature variation and strain evolution, in particular, is coherent with previous studies on thermo-sensitive monitoring techniques for power semiconductor devices, where thermal transients are directly associated with measurable electro-thermo-mechanical responses [23].

As shown in Figure 11, the strain recorded by gauge SG5, located on the Metal Interconnection Tray (MIT), exhibits a strong dependence on temperature, with markedly negative values at low temperatures (down to approximately -600 $\mu$·m$^{-1}$ at -40 $^\circ\text{C}$) and a progressive increase as the temperature rises, reaching positive values of about +200 $\mu$·m$^{-1}$ at +75 $^\circ\text{C}$.

The trend is smooth and continuous, hence reporting a stable response of the measurement system and a consistent deformation behaviour of the structure. Specifically, the graph highlights (i) a compressive peak of about -600 $\mu$·m$^{-1}$ at -40 $^\circ\text{C}$; (ii) a quasi-linear tensile rise reaching $\approx$ +200 $\mu$·m$^{-1}$ at 75 $^\circ\text{C}$; and (iii) a slight hysteresis between the heating and cooling branches, to confirm stable and repeatable thermo-mechanical behaviour.

The moving-average curve closely follows the raw signal, to confirm the reliability of the acquired data and allow a clearer identification of the main deformation pattern (Figure 11 upper). In the positive strain region, the presence of a return branch associated with the cooling phase (from +75 $^\circ\text{C}$ back to room temperature) can be observed, indicating a slight difference between the heating and cooling paths, likely related to thermal inertia and interaction effects within the assembly (Figure 11 lower).

As shown in Figure 12, the strain–temperature behaviour of four key channels reveals a coherent thermo-mechanical response of the assembly. The free gauge SG0 (red) recorded only the bridge’s thermal output, rising almost linearly from about -600 $\mu \varepsilon$ at -30 $^\circ\text{C}$ to slightly above +100 $\mu \varepsilon$ at 75 $^\circ\text{C}$; its smooth trend validated its role as the thermal-compensation reference. The active heat-sink sensor SG1 (blue squares) moved from the same initial compression to roughly +200 $\mu \varepsilon$, crossing zero near 0 $^\circ\text{C}$ and indicating the expected transition from contraction to thermal expansion of the aluminium plate. The interconnection-tray gauge SG5 (black dashed line) followed a nearly parallel trajectory with a small offset, showing that the stack bended coherently with the upper plate while retaining minor stiffness differences. The corrected mean strain M (green triangles), obtained by subtracting SG0 from the arithmetic average of the eight internal gauges, represented the global deformation state. It started at about -1.2 × 10$^3$ $\mu \varepsilon$, climbed steeply, and levelled off just above +300 $\mu \varepsilon$ around 50 $^\circ\text{C}$. The near-linear slopes of SG1 and SG5, together with the consistent convergence of all traces on cooling, suggested a stable thermo-mechanical response. This was a generally effective compensation strategy within the investigated range and limited hysteresis upon return to ambient conditions. Some caution was, nevertheless, required at sub-zero temperatures, in which thermal compensation might remain partial. This aspect, though not affecting the overall interpretation of the strain trends, pointed to the demand for improved compensation strategies in future experimental developments.

In Figure 13a, the three gauges affixed to the upper heat-sink plate, i.e., SG1, its redundant twin SG1R and the centrally located SG2, display a virtually linear strain–temperature relationship. Starting at –30 $^\circ\text{C}$ all sensors register a compressive state of roughly –600 $\mu \varepsilon$; as the temperature rises, they converge toward zero near 0 $^\circ\text{C}$ and enter mild tension above 40 $^\circ\text{C}$, reaching +180 ÷ +250 $\mu \varepsilon$ at 75 $^\circ\text{C}$. The overlap between SG1 and SG1R confirms the excellent repeatability of the redundant pair, while the slightly higher tensile peak of SG2 suggests a marginally larger thermal expansion in the plate’s mid-span.

Figure 13b reports the response of the lower heat-sink plate. The four gauges, SG3, SG3R, SG4 and SG4R, mirror the trend observed on the upper side: An initial compression close to –650 $\mu \varepsilon$ at –30 $^\circ\text{C}$, a monotonic climb through the transition zone, and a final tensile range of +170 ÷ +230 $\mu \varepsilon$ at 75 $^\circ\text{C}$. The redundant couples (SG3/SG3R and SG4/SG4R) overlap almost perfectly, attesting to bonding integrity and stable bridge balance. The small spread between SG3-type and SG4-type readings ($\leq$30 $\mu \varepsilon$ over the full span) indicates that the lower plate experiences a slightly more uniform strain field than the upper one, coherent with its distance from the primary heat sources.

In short, both plates behave elastically and symmetrically under the applied thermo-mechanical cycle, that hysteresis is negligible, and that the redundant gauges provide a reliable check of measurement fidelity across the entire temperature range.

Overall, the results confirmed that the deformation of the heat sink was primarily driven by thermal expansion and constrained by structural configuration, thus providing a coherent basis for comparison with subsequent tests under operating conditions.

The results showed a clear differentiation in the strain response among the monitored locations. Negative strain values (i.e., compressive behaviour) were observed only for strain gauges SG3 and SG4R, whereas all the other gauges exhibited positive strain values, indicating tensile deformation. This suggested a non-uniform deformation pattern, likely associated with the combined effects of thermal gradients, mechanical constraints, and the specific positioning of the measurement points.

Assuming a representative strain level of approximately 500 $\mu$·m$^{-1}$ and considering the distance between the fastening screws as the effective free span of a simply supported beam, a simplified analytical estimation leads to a central deflection of about 1.6 mm. Taking into account the actual structure which behaves as a plate rather than a beam, and that the boundary conditions are more restrictive than simple supports (although not fully clamped), the effective displacement beneath the strain gauges can be reasonably estimated to lie in the range of 0.5 mm to 1 mm.

These results provided a quantitative indication of the deformation levels experienced by the system under realistic operating conditions and confirmed the relevance of thermo-mechanical effects previously identified during the thermal chamber tests.

In Figure 14, signals from representative strain-gauges are displayed. The gauge was wired in a six-tap Wheatstone-bridge circuit, so the acquisition system records included the three upper (excited) arms of the bridge (U1, V1, and W1) and the complementary lower arms (U1, V1, and W1). The red curve is the differential output of the full bridge, i.e., the true strain response of strain-gauges, while the five thinner traces plot the partial voltages of the individual arms. Monitoring these auxiliary channels confirmed that the bridge remaind well balanced and that each arm followed the same thermal-power sequence. The blue-shaded band highlights the amplitude reached by one of those arm voltages during the three high-current plateaux. Together, the six traces provide a complete electrical picture of how SG1R reacts throughout the thermo-mechanical cycle.

Table 1 summarises the step-by-step evolution of the thermo-mechanical cycle applied to the instrumented module. The first three columns reported the acquisition time (in hours) and the temperatures measured by the work-piece thermocouple (T1) and by the climatic chamber (T2) to allow the thermal history move from the initial 25 $^\circ\text{C}$ plateau, through the 75 $^\circ\text{C}$ hot dwell, down to the -39 $^\circ\text{C}$ cold soak, and back to hot.

The next ten columns listed the micro-strain ($\mu$·m$^{-1}$) recorded by the distributed strain gauges (SG1–SG5 and their redundant counterparts, SG1R, SG3R, and SG4R). Positive values denote tensile deformation while negatives indicate compression; the data show symmetric tensile peaks of +110 ÷ +135 $\mu$·m$^{-1}$ at 75 $^\circ\text{C}$ and compressive extrema of -510 ÷ -624 $\mu$·m$^{-1}$ during the cold shock. An additional “SG0” column gives the reading of a free and non-bonded reference gauge that reveals occasional electronic drift (e.g., the -312 $\mu$·m$^{-1}$ spike at 16:10).

The last column reported a flag identifying whether a thermal steady state (TSS) had been reached before the line was logged (“YES”) or whether the module was still in transient conditions (“NO”). A steady state was confirmed at every temperature plateau, thus validating the subsequent strain averages.

Taken together, the data illustrated the module’s full strain envelope under realistic service cycling: (i) Rapid and reversible thermal dilatation; (ii) A pronounced and nearly elastic contraction in the cryogenic segment; and (iii) A slight residual hysteresis on the return to ambient conditions. The contrasting responses of the paired heat sink locations, clearly visible in SG2–SG4 versus their redundant positions, further confirmed the asymmetric stiffness distribution foreseen in the design stage.

In these terms, the occurrence of both tensile and compressive strains among different gauges under operating conditions could be explained by the combined effect of thermal gradients, structural constraints, and global bending of the heat sink.

Firstly, the heat sink is subject to non-uniform thermal loading, with localized heat sources generating differential thermal expansion across the plate. Regions experiencing higher temperatures tend to expand more, leading to tensile strains while adjacent cooler or constrained regions may undergo relative contraction or restraint, resulting in compressive strains.

Secondly, the presence of discrete fastening points (screws) introduces localized mechanical constraints. These constraints limit free thermal expansion, especially near the edges or fixing points, inducing compressive stresses in some areas while allowing more free deformation (and thus tensile strain) in less constrained regions.

Thirdly, the overall structural response of the heat sink resembles that of a plate under bending. Due to asymmetric thermal fields and boundary conditions, the component develops out-of-plane deformation (warpage). In such a configuration, (a) one region of the plate is subject to tensile strain, while (b) adjacent areas experience compressive strain.

Finally, local geometric and material interactions (e.g., coupling with the interconnection plate or stiffness differences between upper and lower heat sinks) further contribute to redistributing the strain field, thus amplifying these local differences.

A more detailed comparison between the two heat sinks highlighted a different behaviour, depending on the loading phase. During the tightening test, both heat sinks showed a compressive response consistent with the preload, but the lower heat sink exhibited slightly more compressive values in some areas and a more pronounced response in one of the gauges, to suggest a less uniform tightening load distribution. During thermal cycling, the two heat sinks followed a very similar trend: They started from a compressive state at a low temperature, passed through the transition zone around 0 $^\circ\text{C}$, and reached slight tensile values at a high temperature. This supported the idea of a consistent overall response of the system. However, the upper heat sink appeared to show slightly greater variability, because SG2 reached a slightly higher peak tension than SG1/SG1R, which suggested greater local sensitivity in the central region of the plate. The lower heat sink, however, appeared more uniform: The text itself stated that the dispersion between SG3-type and SG4-type remained within approximately 30 $\mu \varepsilon$, and linked this uniformity to the greater distance from the main heat sources. In short, a similar global thermo-mechanical trend existed, but with slightly higher local non-uniformity in the upper plate and slightly more homogeneous strain distribution in the lower plate.

The present work analyzed the deformation behavior of a heat sink belonging to a power module for automotive applications, subject to PTCE. Experimental investigation was conducted using resistive strain gauges installed at significant points on the component, with the aim of monitoring deformations during the various operating phases. The key objectives of the study are: (i) to quantify the deformations induced by thermo-mechanical loads; (ii) to evaluate the influence of assembly conditions, particularly screw tightening, on the deformation state of the system; and (iii) to identify any critical issues in the measurement system, in order to propose possible improvements for future experimental activities.

The results provided a consistent and physically coherent representation of the thermo-mechanical behaviour of the system under the applied loading conditions. They also highlighted several critical aspects related to the reliability of the instrumentation and the experimental setup, which are reported below:

• All strain gauges showed adequate performance under the applied thermo-mechanical loads.

• None of the recorded signals appeared inconsistent with the expected physical behaviour.

• Some signals exhibited higher variability than expected; this aspect should be further investigated, preferably through improvements in the test setup rather than additional experimental campaigns.

• The temperature indicated by the climatic chamber cannot be considered fully reliable; the use of dedicated thermocouples is strongly recommended.

• Accurate temperature stabilization requires approximately 10 minutes.

• The measurements proved to be reasonably repeatable, with consistent results obtained at the same measurement points (excluding the effects related to thermal stabilization).

• Below 0 $^\circ\text{C}$, the strain gauges are not thermally compensated; therefore, particular care must be taken in both measurement and data interpretation.

• The use of compensation strain gauges, when exposed to the same thermal cycles but not subject to mechanical loads, is necessary.

• It is recommended to include both a free compensation gauge and a second one bonded to a reference plate, to ensure proper thermal compensation.

• No significant stresses induced by the assembly of the modules onto the control unit were observed; the only relevant deformation appeared to be associated with the initial tightening of the power module onto the housing.

• The free plate (heat sink) and the plate integrated within the plastic frame exhibited similar deformation behaviour during thermal cycling in the range of -40 $^\circ\text{C}$ to 75 $^\circ\text{C}$. This suggested that the plastic frame and the bonding process did not significantly constrain or alter the plate deformation under thermal loading.

Finally, several additional insights emerged indirectly from the investigation, including:

• The use of high-quality strain gauges was strongly recommended for this type of sensitive measurement, as lower-quality sensors might adversely affect the results.

• The adoption of protective coatings or semiconductor-based strain gauges could be considered, as their different construction may reduce susceptibility to electrical interference.

• The evaluation of bolt elongation, potentially achievable using cylindrical strain gauges inserted into a hole on the screw head, was considered of limited interest.

• The use of fibre optic strain gauges could also be explored; due to their optical nature, they are inherently immune to electromagnetic interference.