{"id":"1ec9d7ce-b09e-4a1b-b0ea-dc6790b82771","arxiv_id":"2608.07685","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"A quadratic fit of ultrasonic velocity change versus temperature yields the acoustic nonlinearity parameters alpha, beta, and delta using thermal expansion as the driving strain.","lead":"This paper presents a thermal modulation method that extracts three acoustic nonlinearity parameters from how ultrasonic wave speed changes as a material is slowly heated and cooled. The appeal is a simpler, more uniform way to measure damage-sensitive nonlinear parameters than vibration-based acoustic methods.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The method's central identification conflates thermal-strain nonlinearity with the intrinsic temperature dependence of elastic moduli; this contaminates k1 and the extracted β, and the observed δ+≠δ- shows the model is incomplete.","rationale":"The paper is transparent about its algebra and its experimental procedure, and it makes a falsifiable prediction. The central derivation is clean under the stated constitutive model: Eq. (4) follows from Eq. (2) when ε=α_TΔT, and Eqs. (7)-(8) are immediate. The problem is not algebra but physics: the model has no term for intrinsic temperature dependence of elastic moduli. In metals, ultrasonic velocity changes with temperature even at constant strain, and the observed slopes are of the same magnitude as that effect, so Eq. (7) does not identify β. The paper's own data also show δ+ and δ- with opposite signs for steel and concrete, which the model cannot produce; deferring to 'higher-order hysteresis' means δ is not actually determined. These are not mere measurement-noise issues; they invalidate the claim of absolute accuracy. The reader's weakest_assumption is exactly this strain-only assumption, and I agree that it is load-bearing. A targeted test — either subtracting an independently measured intrinsic velocity-temperature coefficient or comparing with a constant-temperature mechanical acoustoelastic measurement — would settle whether the thermal k1 slopes are dominated by strain-mediated nonlinearity or by ordinary thermal softening. Given this unresolved contamination, the reader's rejection is appropriate and no verdict change is needed.","tokens_in":7481,"tokens_out":8410,"duration_ms":90459,"concrete_test":"Recompute Table I after subtracting an independently measured or literature value of d(ln v)/dT at fixed strain for 304 stainless steel and 6061 aluminum before applying Eq. (7). If the corrected k1 changes sign or magnitude by more than 50%, or if the corrected β falls far outside the reported literature range, the thermal-modulation β is an artifact of intrinsic temperature dependence. A complementary check is to measure β on the same specimens by a constant-temperature mechanical acoustoelastic/DAET test over the same static strain range; agreement with the thermal value would support the strain-only assumption, while a systematic mismatch would confirm the concern.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is substituting ε=α_TΔT into Eq. (2) and reading β, α from k1± via Eq. (7). This presumes that temperature affects ultrasonic velocity only through thermal strain, i.e. (∂E/∂T)|_ε=0. No term for direct temperature dependence of E appears in Eq. (2), and the CWI correction only removes the path-length contribution α_TΔT. In metals, the intrinsic velocity-temperature coefficient is of the same order as the observed k1 values (-1.77×10^-4 and -0.93×10^-4 /°C), so k1± may be dominated by ordinary thermal softening rather than by strain-driven nonlinearity. Because the additive intrinsic term enters k1+ and k1- with the same sign, β extracted from -(k1+ + k1-)/α_T is systematically inflated; this plausibly explains steel β=10.7 exceeding the cited 2-4.5 range. The α estimate from k1+ - k1- is less exposed to this particular artifact, but β is central to the claim. Independently, Table I shows δ+ and δ- with opposite signs for steel and concrete; the paper defers this to unmodeled higher-order hysteresis, so Eq. (8) does not determine a unique δ. Both problems undermine the absolute-measurement claim; the intrinsic-temperature effect is the more fundamental one.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a thermal modulation method for determining the acoustic nonlinearity parameters α, β, and δ. A sample is slowly heated and then cooled while ultrasonic wave velocity is monitored; the relative velocity change dv/v is fitted as a quadratic function of temperature on each branch. Using a quasistatic hysteretic constitutive model, the authors identify β and α with combinations of the linear fit coefficients k1± and δ with the quadratic coefficients k2±. Experiments on aluminum, steel, intact concrete, and ASR-damaged concrete are reported, and the extracted parameters are compared with literature values. The central claim is that this simple, uniform thermal strain field yields absolute values of α, β, and δ.","tokens_in":7780,"tokens_out":5202,"duration_ms":57867,"significance":"If valid, the method would be practically attractive: thermal excitation produces a large, uniform, slowly varying strain field, and CWI gives high-precision velocity measurements. The algebraic path from Eq. (2) to Eqs. (7)–(8) is transparent, and the inclusion of both classical metals and mesoscopic concrete, with an ASR damage contrast, gives the paper a plausible NDE application. However, the load-bearing identification is currently compromised by two unresolved issues: the unseparated intrinsic temperature dependence of elastic moduli, and an unexplained sign mismatch in δ+ versus δ−. The validation is also weaker than claimed because the extracted quantities are algebraic functions of the very coefficients obtained from the same fits. The paper does not provide code, machine-checked proofs, or falsifiable predictions beyond the fits themselves.","major_comments":[{"comment":"The derivation substitutes ε = α_T ΔT into Eq. (2) and reads β and α from k1± via Eq. (7). This presumes that temperature affects ultrasonic velocity only through thermal strain, i.e., that the intrinsic temperature dependence of elastic modulus at fixed strain is negligible. No such term appears in Eq. (2), and the CWI correction dv/v = −(δt − α_T ΔT) removes only the thermal-expansion path contribution, not modulus softening with temperature. The reported k1 values, −1.77×10⁻⁴ /°C for aluminum and −0.93×10⁻⁴ /°C for steel, are of the same order as ordinary thermoelastic velocity-temperature coefficients, so k1± may be dominated by thermal softening rather than by strain-driven nonlinearity. Because an additive intrinsic term enters k1+ and k1− with the same sign, the β value from −(k1+ + k1−)/α_T would be systematically inflated; this is consistent with β = 10.7 for steel lying well above the cited range of 2–4.5. A control experiment separating thermal-strain nonlinearity from (∂V/∂T) at fixed strain, or an independent measurement of the intrinsic modulus-temperature term, is required before absolute β can be claimed.","section":"Theoretical model, Eqs. (2)–(7); CWI paragraph"},{"comment":"The model predicts δ+ = δ−, because the ε² contribution to Eq. (4) is identical in heating and cooling. Table I reports δ+ = 3875 and δ− = −4009 for steel, i.e., opposite signs, and Table II shows the same pattern for concrete. This sign reversal is not explained by the equations presented. The text appeals to a 'higher order hysteretic response (~ε²)' attributed to Meurer et al., but no modified constitutive equation or derivation is given. Consequently, Eq. (8) does not determine a unique δ for the materials tested, and the reported δ± values are not predictions of the model. The paper should either extend Eq. (4) to include the higher-order term explicitly and re-derive Eq. (8), or present δ as an unresolved model limitation.","section":"Eq. (8) and Table I"},{"comment":"The validation is largely circular: β, α, and δ are defined as algebraic functions of the fitted polynomial coefficients, so a good quadratic fit does not independently confirm the model. The claimed 'reasonable agreements' with literature are also weakly supported: for aluminum β = 15.4 is above the cited upper value of 12, and for steel β = 10.7 is more than twice the cited upper value of 4.5, with no uncertainty bars or repeated-sample statistics. A stronger validation would predict at least one quantity not used in the fits, for example the closure gap Δ(dv/v) = α α_T ΔT01 or the cooling branch from the heating-branch coefficients, and then compare that prediction with the measured curve.","section":"Experimental validation, Tables I–II"}],"minor_comments":[{"comment":"The preprint note states that the slight steel hysteresis is due to a temperature measurement error rather than material response, yet Table I reports α = 0 from the equality of k1+ and k1−. Please clarify how the measurement error was identified and why it does not affect the reported k1 values.","section":"Fig. 3 caption and Table I"},{"comment":"The table headers do not state units for k1 and k2, and no confidence intervals are given for the fit coefficients or for the derived β, α, and δ. Please add units and uncertainties.","section":"Tables I and II"},{"comment":"The phrase 'slightly larger' for the β values understates the discrepancies in Table I; steel β = 10.7 is ~2.4 times the upper literature bound of 4.5. The wording should be revised to match the numerical comparison.","section":"Discussion after Table I"},{"comment":"For a measurement-method paper, a data availability statement of 'available from the corresponding author upon reasonable request' is weak; please include at least the processed dv/v–T curves and fit coefficients as supplementary material.","section":"Data availability"}],"recommendation":"reject","confidential_remarks":"The header of the manuscript contains a 'Published as' note identifying it as Appl. Phys. Lett. 116, 241901 (2020). If this manuscript is being submitted as new work, the editor should check prior-publication and overlap policy. Independently of that issue, the technical objections in the major comments concern load-bearing assumptions that would require new experiments or a new model to resolve, not merely local revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper proposes something genuinely new: use a slow thermal cycle to strain the material and extract the nonlinear acoustic parameters α, β, δ from the quadratic fit of dv/v versus T. The setup is simple, the derivation from the McCall–Guyer model is clean, and the concrete results are actually encouraging—the control sample gives β=100 within the literature range, and the α calculated from the gap between heating and cooling curves (40 and 73) matches well with the α from slope differences (36 and 57). That internal consistency is real evidence the method has some sensitivity to hysteresis.\n\nThe soft spots are not minor, though. The central substitution ε=α_TΔT into Eq. (2) assumes temperature affects velocity only through thermal strain. But elastic moduli of metals and concrete also depend on temperature at fixed strain, and the observed k1 values are the same order as that intrinsic temperature coefficient. If there is an additive term cΔT in dv/v, then the extracted β from −(k1⁺+k1⁻)/α_T picks up a spurious contribution of −2c/α_T. That plausibly explains why steel β=10.7 exceeds the cited 2–4.5 range. The paper mentions the discrepancy but attributes it to strain range, not to a missing physical term; that is a gap in the argument. The δ results are also a real problem: the model predicts equal δ⁺ and δ⁻, but steel and concrete show opposite signs. The paper acknowledges this and defers to unmodeled higher-order hysteresis, but without a derivation, Eq. (8) doesn't actually determine a unique δ. There are also no error bars or repeatability measurements, and the arXiv note attributing steel hysteresis to “minor temperature measurement error” is hand-wavy.\n\nWhat holds up? The concept is novel and the experiments demonstrate strong, repeatable-looking correlations. For concrete, the damage sensitivity (ASR > control for α, β, δ) is consistent with known nonlinear behavior. The paper would be a useful contribution if the authors either separated the intrinsic modulus-temperature effect experimentally or reframed the method as a relative damage indicator rather than absolute parameter measurement.\n\nFor peer review: send it out. The idea deserves referee time and the flaws are identifiable and fixable, but the current absolute-accuracy claim is not supported. A serious referee should push for a control measurement of modulus versus temperature, error bars, and a proper treatment of the δ asymmetry.","headline":"Clever idea—thermal strain as the driver for nonlinear acoustic parameters—but the analysis ignores intrinsic temperature dependence of modulus, which likely inflates β, and the δ anomaly shows the model is incomplete; worth a serious referee, not publication as-is.","tokens_in":779,"tokens_out":805,"would_cite":true,"duration_ms":35943,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper establishes that a slow heating–cooling cycle, with a quadratic fit to relative velocity change versus temperature, yields absolute values of the acoustic nonlinearity parameters α, β, and δ for metals and concrete.","keywords":["acoustic nonlinearity","thermal modulation","ultrasonic velocity","coda wave interferometry","hysteresis","concrete damage","nonlinear parameters","thermal strain"],"falsifier":"Measure dv/v versus T on a sample whose modulus has a known intrinsic temperature dependence at fixed strain (for example, a single-crystal whose elastic constants are measured by Brillouin scattering), and compare the fitted β, α, δ with values from an independent mechanical-excitation method on the same sample; if they differ beyond uncertainty, the coefficients mix thermal-strain nonlinearity with a temperature-driven modulus effect.","tokens_in":7248,"feed_emoji":"🌡️","tokens_out":5389,"duration_ms":46132,"temperature":0.7,"pith_summary":"This paper establishes that a slow heating–cooling cycle is enough to measure the absolute values of the three acoustic nonlinearity parameters α, β, δ that describe a material's strain-dependent and hysteretic modulus. Temperature change generates a thermal strain ε = α_T ΔT that drives the nonlinear response, and the relative ultrasonic velocity change dv/v varies quadratically with ΔT. Fitting that quadratic separately for heating and cooling gives coefficients from which β and α are obtained from the average and difference of the linear slopes, and δ from the curvature. Tests on aluminum, steel, intact concrete, and concrete damaged by alkali-silica reaction produce parameter values consistent with literature, with damage increasing all three parameters. The method turns temperature from an unwanted noise source into a uniform, slow, large-strain excitation that needs only a simple ultrasonic setup.","feed_headline":"One heat-cool cycle extracts absolute acoustic nonlinearity","feed_subtitle":"A quadratic fit to relative velocity versus temperature yields alpha, beta, and delta for metals and concrete.","key_machinery":"The load-bearing mechanism is a quadratic polynomial model for the dv/v–temperature curve combined with the hysteresis-capable constitutive law. The paper posits dv/v(±)=k0±+k1± ΔT+k2± ΔT² and links the coefficients to the nonlinear parameters by substituting the thermal strain ε=α_T ΔT into the strain- and strain-rate-dependent modulus expression. Coda wave interferometry supplies the precise relative velocity change (precision ~10⁻⁶) that makes the coefficient extraction meaningful.","core_discovery":"The central claim is that the acoustic nonlinearity parameters α, β, and δ can be recovered directly from the correlation between relative ultrasonic velocity change and temperature in a thermal modulation test. Using a strain- and strain-rate-dependent modulus model E(ε,ε̇)=E0{1 − βε − δε² − α[Δε + ε sign(ε̇)]}, the paper derives that on heating and cooling the relative velocity change follows dv/v(±) = −(1/2){β α_T ΔT + δ α_T² ΔT² + α(α_T ΔT01 ± α_T ΔT)}, where α_T is the thermal expansion coefficient. Comparing this with the fitted quadratic dv/v = k0 + k1± ΔT + k2± ΔT² gives β = −(k1− + k1+)/α_T, α = −(k1+ − k1−)/α_T, and δ± = −2k2±/α_T². The paper validates these relations experimentally: metals yield k1+ = k1− and hence α = 0, while concrete shows hysteresis and damage-dependent increases in α, β, and δ.","pith_inferences":["If the thermal-only assumption holds, the method could be applied to any material with a known thermal expansion coefficient, turning standard temperature-cycle ultrasonic monitoring into a quantitative nonlinearity measurement without adding actuators.","The sign and magnitude difference between δ+ and δ− might be used to isolate the higher-order hysteresis term of the general model; fitting a higher-order polynomial could quantify that term directly.","The strong damage sensitivity on concrete suggests a field application: ambient daily temperature cycles, rather than lab-controlled chambers, might suffice for estimating microcrack density in structures.","The formulas assume the same thermal strain in the wave path and in the constitutive model; tests at different heating rates could reveal whether the extracted parameters are rate-independent, which the current quasi-static assumption implies but does not prove."],"forward_implications":["A single thermal cycle, with temperature held at about 1 °C/h to keep strain uniform, yields absolute values of α, β, and δ without the calibration needed in harmonic-generation methods.","For non-hysteretic metals, equal heating and cooling slopes directly imply α = 0, providing an internal consistency check of the method.","Concrete damaged by alkali-silica reaction shows larger |k1±| and |k2±| than intact concrete, so the fitted coefficients themselves could serve as damage indicators.","Because the curvature terms δ+ and δ− differ in sign and magnitude for concrete, the model points to a higher-order (∼ε²) hysteretic contribution as predicted by the general nonlinear constitutive theory."],"supporting_citations":[{"why":"Supplies the strain- and strain-rate-dependent modulus model (Eq. 2) from which the parameter relations are derived.","marker":"4"},{"why":"Provides the coda wave interferometry method used to measure relative velocity changes to 10⁻⁶ precision.","marker":"16"},{"why":"Prior work establishing temperature-induced velocity changes in concrete and the thermal modulation coefficient that this method builds on.","marker":"12"},{"why":"Reports concrete β values used as literature comparison for the control sample.","marker":"15"},{"why":"Another concrete β literature value used for comparison.","marker":"22"},{"why":"Provides the order-of-magnitude rock δ value used to compare concrete results.","marker":"23"},{"why":"General nonlinear model that predicts higher-order hysteresis, referenced for interpreting δ+ versus δ− differences.","marker":"3"}],"fun_headline_variants":["Thermal strain exposes acoustic nonlinearity parameters","Heat-cool cycle unlocks alpha, beta, delta via ultrasound","Temperature sweep yields absolute nonlinearity from wave velocity","One thermal cycle quantifies material nonlinearity simply"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The derivation assumes that temperature changes the ultrasonic velocity only by producing thermal strain that acts through the material's strain-dependent modulus, and that the elastic modulus itself does not change with temperature at fixed strain.","fun_headline_variants_meta":{"raw":{"variants":["Thermal strain exposes acoustic nonlinearity parameters","Heat-cool cycle unlocks alpha, beta, delta via ultrasound","Temperature sweep yields absolute nonlinearity from wave velocity","One thermal cycle quantifies material nonlinearity simply"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000323,"raw_usage":{"total_tokens":1838,"prompt_tokens":993,"completion_tokens":845,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":609,"completion_tokens_details":{"reasoning_tokens":785}},"tokens_in":609,"tokens_out":845,"duration_ms":8892,"temperature":1.0,"reasoning_tokens":785,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T00:24:49.368471+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure dv/v versus T on a sample whose modulus has a known intrinsic temperature dependence at fixed strain (for example, a single-crystal whose elastic constants are measured by Brillouin scattering), and compare the fitted β, α, δ with values from an independent mechanical-excitation method on the same sample; if they differ beyond uncertainty, the coefficients mix thermal-strain nonlinearity with a temperature-driven modulus effect.","supporting_citations":[{"cited_title":"The Journal of the Acoustical Society of America , volume=","cited_arxiv_id":null,"evidence_quote":"Supplies the strain- and strain-rate-dependent modulus model (Eq. 2) from which the parameter relations are derived."},{"cited_title":"Science , volume=","cited_arxiv_id":null,"evidence_quote":"Provides the coda wave interferometry method used to measure relative velocity changes to 10⁻⁶ precision."},{"cited_title":"The Journal of the Acoustical Society of America , volume=","cited_arxiv_id":null,"evidence_quote":"Prior work establishing temperature-induced velocity changes in concrete and the thermal modulation coefficient that this method builds on."},{"cited_title":"Ultrasonics , volume=","cited_arxiv_id":null,"evidence_quote":"Reports concrete β values used as literature comparison for the control sample."},{"cited_title":"Review of Progress in Quantitative Nondestructive Evaluation , pages=","cited_arxiv_id":null,"evidence_quote":"Another concrete β literature value used for comparison."},{"cited_title":"Ultrasonics , volume=","cited_arxiv_id":null,"evidence_quote":"Provides the order-of-magnitude rock δ value used to compare concrete results."},{"cited_title":"and Guyer, Robert , year =","cited_arxiv_id":null,"evidence_quote":"General nonlinear model that predicts higher-order hysteresis, referenced for interpreting δ+ versus δ− differences."}],"review_version":1}