Direct Current Potential Drop (DCPD)

• DCPD is an electrical crack-monitoring method that applies a constant current and measures the resulting voltage drop to assess crack initiation, growth, and closure.
• The technique leverages Ohm’s law with calibration via analytical and finite-element models to convert voltage changes into quantifiable crack dimensions.
• DCPD is valued for its robustness and real-time monitoring capabilities in high-temperature, high-pressure, and electromagnetically noisy environments, despite lower sensitivity to very short cracks.

Direct Current Potential Drop (DCPD) is an electrical crack-monitoring technique in which a constant direct current is injected through a conductive specimen and the voltage drop between probes spanning the crack region is measured. Crack initiation, crack growth, crack opening, and crack-face contact perturb the current field and modify the effective electrical resistance, so the measured potential drop varies in a way that can be calibrated to crack size or interpreted in relation to crack closure. In fatigue testing, DCPD is used for real-time monitoring from initiation into the Paris regime, and it is particularly valued for robustness in harsh, electromagnetically noisy, high-temperature, and high-pressure environments, although it is less sensitive than AC potential drop (ACPD) to very short cracks (Hambardzumyan et al., 28 Sep 2025, Keesler-Evans et al., 2021).

1. Physical basis and governing relations

The core DCPD relation is Ohm’s law,

$V = I R,$

with a constant injected current $I$ and a measured potential drop $V$. For a uniform conductor, resistance is written as

$R = \rho \frac{L}{A},$

or, in the crack-opening/closure context,

$R = \rho \frac{L}{S_{\text{uncracked}}},$

where $\rho$ is the electrical resistivity, $L$ is the gauge length, and $A$ or $S_{\text{uncracked}}$ is the effective conducting cross-section. A crack reduces the available conducting ligament and perturbs the potential field, so at fixed current the potential drop rises as the crack grows or opens further (Hambardzumyan et al., 28 Sep 2025, Asselin et al., 16 Jun 2026).

The field description used in the low-cycle-fatigue closure study is

$E = \frac{J}{\sigma}, \qquad V = \int E \cdot dl,$

with $I$0 the electrical conductivity and $I$1. In this representation, the crack acts as an internal barrier that forces current lines to detour around the crack front, increasing current density in the remaining ligament and increasing the measured potential drop. When crack faces contact during compression, local conduction across the crack plane partially bypasses the open-crack path, reducing the potential drop relative to the fully open state (Asselin et al., 16 Jun 2026).

Several normalized forms are used. A constant-current formulation implies the normalized potential drop

$I$2

which is used for calibration and drift rejection. Other studies normalize by an initial or uncracked reference voltage, for example

$I$3

where $I$4 is the baseline potential drop at a reference crack length or in an uncracked calibration model (Hambardzumyan et al., 28 Sep 2025, Asselin et al., 16 Jun 2026). The crack-length relation is geometry-specific and is therefore expressed generically as

$I$5

or, in normalized polynomial form,

$I$6

with $I$7 the specimen width and $I$8 calibration constants (Keesler-Evans et al., 2021).

Two clarifications are central. First, DCPD is monotonic with crack growth under fixed conditions, but the signal does not depend on crack length alone: temperature, strain-dependent resistivity, crack-face electrical bridging, and magnetostriction in ferromagnetic steels can also alter the measured potential drop (Hambardzumyan et al., 28 Sep 2025, Asselin et al., 16 Jun 2026). Second, DCPD provides an averaged electrical response to the crack configuration; where multiple small cracks are present, it reflects an average crack effect and cannot identify which crack will dominate (Hambardzumyan et al., 28 Sep 2025).

2. Instrumentation, probe topology, and calibration

A DCPD system comprises a stable constant-current source, current injection leads, voltage probes spanning a defined gauge length, and a sensitive differential voltage measurement chain. Because metallic specimens have low resistance and the voltage changes associated with crack advance are small, the instrumentation typically uses a high-precision voltmeter or instrumentation amplifier with high-resolution ADC acquisition. Standard DCPD practice cited in the IN718 machine-learning study uses a four-wire (Kelvin) configuration, with two current leads for excitation and two separate voltage leads sensing the local potential drop so that lead and contact resistances minimally influence the voltage measurement (Keesler-Evans et al., 2021).

Probe placement controls both sensitivity and signal level. Smaller voltage-probe spacing increases the change in potential drop per unit crack growth, improving resolution, but reduces the absolute voltage and therefore increases susceptibility to electronic noise. Sensitivity also increases with injected current $I$9 and resistivity $V$0, but current escalation is constrained by heating and drift. In practice, spot welding is commonly used for probe attachment, and stable electrical contacts are essential for long-duration experiments (Hambardzumyan et al., 28 Sep 2025).

Calibration is indispensable because the $V$1-to-$V$2 relation depends on geometry, probe placement, and current path. Analytical solutions, Johnson-equation-based calibrations, finite-element electrostatic or thermoelectric analogies, and empirical procedures such as sawn cuts, marker loads, and crack-front marking are all used. A recurring limitation is that analytical expressions can underestimate crack length for curved crack fronts, so finite-element calibration is preferred for curved or complex geometries (Hambardzumyan et al., 28 Sep 2025, Keesler-Evans et al., 2021).

The two detailed specimen-specific calibration routes in the supplied literature illustrate this dependence. In the IN718 fatigue studies, crack length was correlated with probe potential using a calibration function derived from specimen geometry and Johnson’s equations, and a finite-element electrostatic calibration was ultimately adopted for the custom rectangular compact specimen (Keesler-Evans et al., 2021, Lindsay et al., 2019). For that geometry, the working conversion used in data reduction was

$V$3

with

$V$4

and $V$5 in millimeters (Lindsay et al., 2019).

In the 18MND5 low-cycle-fatigue closure study, calibration was constructed from a combined experimental-numerical procedure. Experimental crack fronts were marked by acrylic ink during the test, the specimen was cryo-fractured in liquid nitrogen at $V$6 to reveal the marked fronts, and each mark provided a $V$7 datum. A Cast3M finite-element “thermoelectric” analogy on a half-gauge model with a semi-elliptic surface crack then produced a continuous mapping between $V$8 and $V$9, where $R = \rho \frac{L}{A},$0 was the EDM notch depth. The largest measured ellipticity ratio was $R = \rho \frac{L}{A},$1 (Asselin et al., 16 Jun 2026).

3. Fatigue crack initiation, propagation, and fracture-mechanics coupling

DCPD has been shown to detect crack initiation in fatigue experiments and to track crack growth in real time. In the IN718 studies, high-rate DCPD measurements captured the time history from crack initiation through the Paris regime, including short crack jumps that occurred predominantly during 100 s hold segments at peak load (Hambardzumyan et al., 28 Sep 2025, Keesler-Evans et al., 2021). The 2019 IN718 study used DCPD as the in-situ monitoring backbone at 512 Hz, and the authors explicitly used the method to quantify crack jumps between successive hold segments under room-temperature and elevated-temperature loading in atmospheric air (Lindsay et al., 2019).

Once calibrated crack length histories are available, DCPD can be coupled directly to fracture-mechanics analysis. The IN718 studies used the single-edge-crack-in-tension expression

$R = \rho \frac{L}{A},$2

with $R = \rho \frac{L}{A},$3 the nominal stress and $R = \rho \frac{L}{A},$4 for the custom geometry (Keesler-Evans et al., 2021, Lindsay et al., 2019). Paris-law analysis was then framed in the usual form

$R = \rho \frac{L}{A},$5

In the 2019 IN718 investigation, DCPD-derived $R = \rho \frac{L}{A},$6 versus $R = \rho \frac{L}{A},$7 data fell in Region II, with Paris exponent $R = \rho \frac{L}{A},$8 and coefficient $R = \rho \frac{L}{A},$9, consistent with the literature cited by the authors (Lindsay et al., 2019). The same work also normalized the per-cycle crack growth by the stress-intensity factor ratio,

$R = \rho \frac{L}{S_{\text{uncracked}}},$0

to account for the increasing driving force as crack length increased (Lindsay et al., 2019).

The time-history character of DCPD is especially important in nonstationary loading protocols. In the 2021 IN718 machine-learning study, tests were performed on an MTS810 hydraulic load frame with 10 triangular oscillations over 30 s at load ratio $R = \rho \frac{L}{S_{\text{uncracked}}},$1, followed by a 100 s hold at peak load; peak loads were 1600 N, 1700 N, and 1800 N. The DCPD stream was sampled at 512 Hz specifically to capture small, rapid crack jumps, and crack jumps were reported to occur predominantly during the hold period (Keesler-Evans et al., 2021). This operational mode differs from lower-rate crack-length methods by preserving transient events rather than only cycle-averaged growth.

4. Crack opening and closure detection

DCPD is also used to detect crack opening and closure during cyclic loading. In the 18MND5 low-cycle-fatigue study, the signal was interpreted over stepped cycles in which the potential drop was recorded during 41 static strain steps. The $R = \rho \frac{L}{S_{\text{uncracked}}},$2–$R = \rho \frac{L}{S_{\text{uncracked}}},$3 curve exhibited two regimes: at more compressive strains there was an initial increase of $R = \rho \frac{L}{S_{\text{uncracked}}},$4 attributed to progressive crack closure, and beyond a knee point the potential varied linearly with strain because resistivity changes with total or plastic strain dominated after contact-state changes ceased (Asselin et al., 16 Jun 2026).

Crack opening strain $R = \rho \frac{L}{S_{\text{uncracked}}},$5 and closure strain $R = \rho \frac{L}{S_{\text{uncracked}}},$6 were defined as the axial strains at which the crack started to open and fully closed, deduced either from H-DIC strain-opening loops or from DCPD strain-voltage loops. In DCPD, these quantities were identified at the slope change between the closure-driven regime and the resistivity-driven linear regime. An algorithmic implementation proposed in the study was to fit linear segments to the high-strain region and detect the strain at which residuals or slope changes exceeded a threshold, or alternatively to detect inflection points in $R = \rho \frac{L}{S_{\text{uncracked}}},$7–$R = \rho \frac{L}{S_{\text{uncracked}}},$8 (Asselin et al., 16 Jun 2026).

The principal result is that, for both imposed strain amplitudes $R = \rho \frac{L}{S_{\text{uncracked}}},$9 and $\rho$0, the crack did not remain fully closed throughout the compressive half-cycle. At $\rho$1 and crack depth $\rho$2, the study reported

$\rho$3

which means that opening and closure occurred within the compressive part of the cycle (Asselin et al., 16 Jun 2026). This directly contradicts the common simplification that a fatigue crack under tension-compression loading is necessarily fully closed throughout the compressive segment.

The same study quantified cycle-based opening fractions as

$\rho$4

and reported that these ratios increased with crack depth and with plastic strain amplitude (Asselin et al., 16 Jun 2026). Opening and closure strains became more negative as the crack grew, indicating that the crack stayed open during a larger fraction of each cycle.

The equivalent cyclic opening stress was obtained by inverting the cyclic Ramberg–Osgood relation

$\rho$5

and results were analyzed in normalized form using

$\rho$6

The reported trend was that $\rho$7 decreased as $\rho$8 approached the flow stress $\rho$9, becoming negative near $L$0, consistent with literature comparisons and with Newman’s plane-stress opening model for $L$1 (Asselin et al., 16 Jun 2026).

A further interpretive point concerns spatial averaging. H-DIC and DCPD yielded similar opening/closure trends, but DCPD tended to give slightly lower opening strains because it integrates contributions from deeper, more plane-strain-dominated regions of the crack front, whereas H-DIC samples the plane-stress-dominated surface opening (Asselin et al., 16 Jun 2026).

5. Performance, sensitivity, uncertainty, and environmental behavior

DCPD performance is governed by calibration quality, probe geometry, signal-to-noise ratio, and environmental stability. The review paper reports typical errors in potential-drop crack-depth measurements of 10–20%, reflecting calibration and environmental uncertainties such as temperature, contact stability, and geometry effects (Hambardzumyan et al., 28 Sep 2025). The method is less sensitive than ACPD to very short cracks, but it has been shown to detect crack initiation in fatigue experiments (Hambardzumyan et al., 28 Sep 2025).

Sensitivity is strongly probe-spacing dependent. Reducing voltage-probe spacing increases the voltage change per unit crack growth but lowers the absolute signal and increases susceptibility to electronic noise. Increasing injected current also increases sensitivity, but Joule heating,

$L$2

introduces drift and may alter specimen temperature, so current must remain low enough to avoid significant self-heating (Hambardzumyan et al., 28 Sep 2025).

Several signal disturbances recur across studies. Temperature changes alter resistivity and therefore modify $L$3 and $L$4; ferromagnetic steels can exhibit magnetostriction (Villari effect), which changes the potential drop independently of crack growth; crack-face contact can create electrical bridges that distort the signal; and general electronic noise becomes important because the absolute voltage across metallic specimens is small (Hambardzumyan et al., 28 Sep 2025). In the 18MND5 closure experiments, an additional complication was that the DCPD signal contained a linear contribution from resistivity increase with total strain and plastic strain, requiring separation of closure-driven and resistivity-driven contributions during stepped-cycle interpretation (Asselin et al., 16 Jun 2026).

Mitigation strategies are correspondingly explicit in the literature. These include temperature control, temperature sensors, temperature-compensation circuits, signal averaging, use of the maximum potential drop per cycle to reduce temperature-related errors and crack-face bridging, stable current sources with feedback, differential voltage measurement, and careful spot welding of probes (Hambardzumyan et al., 28 Sep 2025). In ferromagnetic steels, a practical remedy for magnetostrictive artifacts is the use of non-magnetic materials where possible or a switch to ACPD (Hambardzumyan et al., 28 Sep 2025).

The electrical-noise characterization in the 2019 IN718 study provides a concrete benchmark. A one-hour zero-load DCPD test yielded a Gaussian noise histogram centered about zero after calibration or bias removal; the voltage axis of the histogram spanned approximately $L$5 (Lindsay et al., 2019). The 2021 IN718 machine-learning study, citing prior work, reported random DCPD noise with standard deviation $L$6 and intentionally retained this unfiltered noise so that physically meaningful high-frequency features were preserved (Keesler-Evans et al., 2021). At lower peak loads in the 2019 IN718 dataset, especially $L$7 for that geometry, negative $L$8 artifacts appeared because the signal-to-noise ratio had degraded, not because true crack closure occurred at zero minimum load (Lindsay et al., 2019).

Environmental robustness is a defining advantage. DCPD is highlighted as suitable for high temperature, high pressure, and EMI-heavy conditions, including nuclear reactor components (Hambardzumyan et al., 28 Sep 2025). A specific example is its successful application to stainless-steel bars under simulated pressurized water reactor conditions of $L$9 and 150 bar, where it detected crack initiation and estimated growth rates (Hambardzumyan et al., 28 Sep 2025). This robustness under adverse environments is one reason DCPD remains competitive even where ACPD offers better very-short-crack sensitivity.

6. Integration with high-precision DAQ, machine learning, and multi-sensor monitoring

Recent implementations place DCPD within synchronized high-precision control and data acquisition architectures. The review paper describes constant-current sources with feedback to stabilize $A$0, high-resolution ADCs to capture $A$1 synchronously with load and displacement, temperature-compensation circuits and signal averaging to mitigate drift, and real-time algorithms that convert $A$2 to $A$3 from calibration curves (Hambardzumyan et al., 28 Sep 2025). Closed-loop testing can then maintain constant load, displacement, or stress-intensity factor while DCPD tracks crack length, enabling stable growth experiments in corrosive or high-temperature environments (Hambardzumyan et al., 28 Sep 2025).

The coupling of DCPD with other sensing modalities is technically important because DCPD and complementary methods observe different aspects of crack evolution. The review notes fused analysis with load, displacement, and AE, and reports that DCPD crack-length measurements were used in an AE study to correlate AE features with crack length and stress-intensity-factor range $A$4 (Hambardzumyan et al., 28 Sep 2025). The same review argues that combining DCPD with AE or DIC can improve early initiation detection, source discrimination, and false-positive rejection, particularly where DCPD alone is insensitive to multiple small cracks or very short cracks (Hambardzumyan et al., 28 Sep 2025).

The most explicit data-driven exploitation of DCPD time histories appears in the IN718 BiLSTM study. There, sequences of stress intensity $A$5 and temperature $A$6 were used as inputs to a bidirectional LSTM with 100 units, activation $A$7, recurrent activation $A$8, dropout 0.2, a Dense output layer with 1 unit, MSE loss, Adam optimizer with learning rate 0.0005, batch size 256, and a 90\%/10\% train/validation split with K-fold folding of validation due to concatenation (Keesler-Evans et al., 2021). The target output was crack length $A$9, and the network operated on three-step input sequences to predict the fourth step.

The model achieved mean absolute error on training of $S_{\text{uncracked}}$0 and on validation or test of $S_{\text{uncracked}}$1, reproduced crack jumps and overall crack progression, and predicted intermediate temperatures and stress intensities from crack initiation through the Paris regime (Keesler-Evans et al., 2021). The authors emphasized that unfiltered DCPD signals contain both random measurement noise and physically meaningful high-frequency features likely related to oxidation, grain boundaries, and local crack-tip phenomena; this suggests that DCPD time histories encode mechanistic information beyond a smoothed crack-length trajectory (Keesler-Evans et al., 2021). A plausible implication is that DCPD can serve not only as a crack-length channel but also as a data source for hybrid physics-informed and sequence-learning models when calibration fidelity is preserved.

From an applied standpoint, the literature supports a consistent operational doctrine. Use a stable constant-current source with feedback; record $S_{\text{uncracked}}$2 explicitly so that $S_{\text{uncracked}}$3 can be computed; synchronize $S_{\text{uncracked}}$4, $S_{\text{uncracked}}$5, load, and displacement within the DAQ; calibrate the specific geometry by FEA and/or empirical crack-front measurements; manage temperature and Joule heating; and validate DCPD-derived crack lengths against independent methods where feasible (Hambardzumyan et al., 28 Sep 2025). In low-cycle-fatigue crack-closure studies, a coupled DCPD–H-DIC strategy is particularly effective: DCPD tracks crack depth and global closure behavior, while H-DIC resolves surface opening near the tip and extends sensitivity to shallower cracks (Asselin et al., 16 Jun 2026).

DCPD is therefore best understood as a calibrated electrical field measurement that links specimen-scale conduction physics to crack mechanics. Its strongest applications arise where continuous in-situ monitoring, harsh-environment tolerance, high temporal resolution, and compatibility with synchronized control or data-fusion architectures are required, provided that geometry-specific calibration, thermal management, and contact stability are treated as first-order experimental variables (Hambardzumyan et al., 28 Sep 2025, Lindsay et al., 2019).