Cross Direction: Critical Dimension in Steel Sheet Processing & Quality

Definition and Basic Concept

Cross Direction (CD) refers to the direction perpendicular to the primary processing or rolling direction in sheet or strip steel products. It represents one of the principal directional properties in flat steel products, with the other being the Rolling Direction (RD) or Machine Direction (MD). Cross Direction properties are critical in understanding and predicting the anisotropic behavior of steel materials during forming operations.

The concept of Cross Direction is fundamental in materials processing as it directly influences mechanical properties, dimensional stability, and formability of steel products. Due to the directional nature of rolling processes, steel exhibits different properties when tested in the Cross Direction versus the Rolling Direction.

Within the broader field of metallurgy, Cross Direction represents a key aspect of material anisotropy, which is the property of materials to exhibit different characteristics along different axes. Understanding Cross Direction properties is essential for predicting material behavior in complex forming operations and for designing steel products with optimal performance characteristics.

Physical Nature and Theoretical Foundation

Physical Mechanism

At the microstructural level, Cross Direction properties emerge from the alignment of grains, inclusions, and crystallographic textures during the rolling process. When steel is rolled, grains become elongated in the rolling direction and compressed in the cross direction, creating a preferred crystallographic orientation or texture.

This directional microstructure results from plastic deformation during rolling, where slip systems within crystal structures activate along preferred orientations. The distribution of dislocations, grain boundaries, and second-phase particles becomes non-uniform between the rolling and cross directions.

The anisotropy between Cross Direction and Rolling Direction is further influenced by the distribution of inclusions, which tend to align along the rolling direction, creating planes of weakness that affect mechanical properties differently in the cross direction.

Theoretical Models

The primary theoretical framework for describing Cross Direction properties is the anisotropic plasticity theory, particularly the Hill's anisotropic yield criterion developed by Rodney Hill in 1948. This model extends the von Mises yield criterion to account for directional differences in material properties.

Historically, understanding of Cross Direction evolved from simple empirical observations in the early steel industry to sophisticated crystallographic texture analysis in the mid-20th century. Early steel producers noticed directional differences in sheet metal forming but lacked theoretical explanations.

Modern approaches include the Barlat yield criterion and crystal plasticity models, which provide more accurate predictions for complex loading conditions compared to Hill's model, especially for advanced high-strength steels with complex microstructures.

Materials Science Basis

Cross Direction properties are intimately related to the crystal structure of steel, particularly the orientation distribution of crystal lattices (texture). In body-centered cubic (BCC) iron, specific crystallographic planes tend to align parallel to the rolling plane, creating anisotropy.

The grain boundaries in rolled steel typically have elongated morphologies in the rolling direction, creating different boundary densities when measured in the cross direction. This affects dislocation movement and consequently mechanical properties.

The fundamental materials science principle of structure-property relationships is exemplified in Cross Direction phenomena, where processing-induced microstructural directionality directly translates to macroscopic property differences that engineers must account for in applications.

Mathematical Expression and Calculation Methods

Basic Definition Formula

The anisotropy in sheet metals is commonly quantified using the Lankford coefficient or r-value:

$$r = \frac{\varepsilon_w}{\varepsilon_t}$$

Where $\varepsilon_w$ is the true strain in the width direction and $\varepsilon_t$ is the true strain in the thickness direction during a tensile test.

The r-value specifically for the Cross Direction is denoted as $r_{90}$, indicating measurement at 90° to the rolling direction.

Related Calculation Formulas

The normal anisotropy ($\bar{r}$) and planar anisotropy ($\Delta r$) can be calculated using:

$$\bar{r} = \frac{r_0 + 2r_{45} + r_{90}}{4}$$

$$\Delta r = \frac{r_0 - 2r_{45} + r_{90}}{2}$$

Where $r_0$, $r_{45}$, and $r_{90}$ are r-values measured at 0°, 45°, and 90° to the rolling direction, respectively.

These formulas are applied to predict forming behavior, with higher $\bar{r}$ values indicating better deep drawability and $\Delta r$ values closer to zero indicating more uniform forming properties.

Applicable Conditions and Limitations

These formulas assume homogeneous material properties within each direction and are most valid for low to moderate strain levels (typically below 20%).

The models have limitations when applied to advanced high-strength steels with complex phase structures or when strain paths change during forming operations.

The calculations assume isothermal conditions and do not account for strain rate sensitivity, which becomes significant at high forming speeds or elevated temperatures.

Measurement and Characterization Methods

Standard Testing Specifications

ASTM E517: Standard Test Method for Plastic Strain Ratio r for Sheet Metal - Provides the primary methodology for determining r-values in different directions.

ISO 10113: Metallic materials - Sheet and strip - Determination of plastic strain ratio - Offers international standards for measuring directional properties.

ASTM E8/E8M: Standard Test Methods for Tension Testing of Metallic Materials - Specifies procedures for tensile testing that can be adapted for cross-directional testing.

JIS Z 2254: Method of tensile test for metallic materials - Japanese standard that includes provisions for directional testing of sheet metals.

Testing Equipment and Principles

Universal testing machines equipped with extensometers capable of measuring strain in multiple directions simultaneously are commonly used for Cross Direction testing.

Optical strain measurement systems using digital image correlation (DIC) provide full-field strain mapping, allowing precise measurement of width and thickness strains during testing.

Specialized tooling including grips designed to minimize slippage and ensure proper alignment is essential for accurate Cross Direction testing, particularly for high-strength materials.

Sample Requirements

Standard tensile specimens are typically cut with their long axis perpendicular to the rolling direction, with dimensions conforming to ASTM E8 or ISO 6892-1 standards.

Surface preparation generally requires minimal intervention beyond degreasing, though edge quality is critical to prevent premature failure.

Specimens must be clearly marked to indicate orientation relative to the original sheet, and multiple specimens are typically tested to account for material variability.

Test Parameters

Testing is typically conducted at room temperature (23 ± 5°C) unless specific elevated or low-temperature properties are being evaluated.

Standard strain rates range from 0.001 to 0.008 s⁻¹ for quasi-static testing, with higher rates used for dynamic property assessment.

Humidity should be controlled within 30-70% relative humidity to minimize environmental effects on test results.

Data Processing

Data collection typically involves simultaneous recording of load, extension, width change, and sometimes thickness change at frequencies of 5-10 Hz or higher.

Statistical analysis typically includes calculating mean values and standard deviations from multiple specimens, with outlier analysis according to ASTM E178.

Final r-values are calculated from the slope of the width strain versus thickness strain curve in the plastic deformation region, typically between 5% and 15% elongation.

Typical Value Ranges

Steel Classification	Typical r₉₀ Value Range	Test Conditions	Reference Standard
Low Carbon Steel	1.0-1.8	Room temp, 0.002 s⁻¹	ASTM E517
IF (Interstitial Free) Steel	1.6-2.5	Room temp, 0.002 s⁻¹	ASTM E517
HSLA Steel	0.8-1.2	Room temp, 0.002 s⁻¹	ASTM E517
TRIP Steel	0.7-1.0	Room temp, 0.002 s⁻¹	ISO 10113

Variations within each classification typically result from differences in processing history, particularly the degree of cold reduction and annealing parameters.

Higher r₉₀ values generally indicate better formability in the Cross Direction, which is particularly important for components with significant deformation perpendicular to the rolling direction.

A notable trend is that steels designed specifically for deep drawing applications (like IF steels) exhibit higher r-values in all directions compared to structural grades like HSLA steels.

Engineering Application Analysis

Design Considerations

Engineers typically incorporate Cross Direction properties into forming simulations using finite element analysis with anisotropic material models to predict thinning and potential failure locations.

Safety factors of 1.2 to 1.5 are commonly applied to account for material variability and limitations in predicting complex strain paths during forming operations.

Material selection decisions often prioritize balanced directional properties (low Δr) for complex parts, while maximizing normal anisotropy (high r̄) for deep drawn components.

Key Application Areas

Automotive body panels represent a critical application area where Cross Direction properties directly impact formability, particularly for complex geometries with multi-directional stretching requirements.

Appliance manufacturing utilizes Cross Direction properties differently, often focusing on consistent surface appearance and dimensional stability rather than extreme formability.

Packaging applications, particularly food cans, require specific Cross Direction properties to ensure uniform wall thickness during the drawing and ironing processes that form cylindrical containers.

Performance Trade-offs

Higher strength steels typically exhibit lower r-values in the Cross Direction, creating a fundamental trade-off between strength and formability that engineers must balance.

Improved Cross Direction formability often comes at the expense of surface quality, as the processing required to enhance r-values can lead to orange peel or other surface imperfections.

Engineers frequently balance Cross Direction properties against cost considerations, as achieving optimal directional properties may require additional processing steps or more expensive alloying elements.

Failure Analysis

Splitting or tearing along the Rolling Direction represents a common failure mode related to insufficient Cross Direction properties, particularly during stretch-forming operations.

This failure mechanism typically initiates at areas of localized thinning and progresses rapidly once the material exceeds its strain limit in the Cross Direction.

Mitigating these risks involves optimizing blank geometry, using appropriate lubricants, and potentially selecting materials with higher r₉₀ values for challenging geometries.

Influencing Factors and Control Methods

Chemical Composition Influence

Carbon content significantly impacts Cross Direction properties, with lower carbon generally improving r-values through reduced interstitial strengthening mechanisms.

Titanium and niobium as microalloying elements enhance Cross Direction properties by forming carbides and nitrides that prevent interstitial elements from restricting dislocation movement.

Phosphorus additions can improve r-values in low-carbon steels but must be carefully controlled to avoid embrittlement issues.

Microstructural Influence

Finer grain sizes typically reduce the anisotropy between Rolling Direction and Cross Direction properties by minimizing the impact of crystallographic texture.

Phase distribution significantly affects Cross Direction properties, with single-phase materials generally exhibiting more predictable anisotropic behavior than multi-phase steels.

Non-metallic inclusions, particularly those elongated in the rolling direction, create planes of weakness that can dramatically reduce Cross Direction mechanical properties.

Processing Influence

Annealing treatments, particularly batch annealing versus continuous annealing, significantly influence Cross Direction properties through their effect on recrystallization and texture development.

Cold rolling reduction ratio directly impacts Cross Direction properties, with higher reductions typically increasing anisotropy unless followed by appropriate recrystallization annealing.

Cooling rates after hot rolling or annealing affect phase transformations and precipitation behavior, thereby influencing the final Cross Direction properties.

Environmental Factors

Elevated temperatures generally reduce the difference between Rolling Direction and Cross Direction properties due to increased dislocation mobility in all directions.

Hydrogen environments can exacerbate anisotropic behavior through preferential diffusion along elongated grain boundaries or inclusion interfaces.

Strain aging over time can increase directional differences, particularly in steels with free interstitial elements that can migrate to dislocations.

Improvement Methods

Texture engineering through controlled rolling schedules and precise temperature control during processing represents a metallurgical approach to optimize Cross Direction properties.

Skin pass rolling with carefully controlled reduction percentages (typically 0.5-2%) can improve Cross Direction formability by introducing beneficial dislocation structures.

Component design approaches that align major forming strains with favorable material directions can compensate for inherent Cross Direction limitations.

Related Terms and Standards

Related Terms

Planar Anisotropy refers to the variation of properties in the plane of the sheet, quantified by the Δr value, which directly relates to Cross Direction behavior.

Earing is a phenomenon during deep drawing where the material forms an uneven top edge with peaks and valleys due to directional differences in properties.

Normal Anisotropy (r̄) represents the average resistance to thinning across all directions in the sheet plane and complements Cross Direction measurements.

Crystallographic Texture describes the preferred orientation of crystal lattices that fundamentally causes the differences between Cross Direction and Rolling Direction properties.

Main Standards

ISO 10113:2020 provides the international standard methodology for determining plastic strain ratios in metallic sheet materials across different directions.

ASTM A1008/A1008M covers the specification for steel sheet, cold-rolled, carbon, structural, high-strength low-alloy with improved formability, which includes requirements related to directional properties.

EN 10130 is the European standard for cold-rolled low carbon steel flat products for cold forming, which includes provisions for testing and specifying Cross Direction properties.

Development Trends

Advanced characterization techniques including in-situ neutron diffraction are enabling deeper understanding of texture evolution during deformation in the Cross Direction.

Machine learning approaches are emerging to predict Cross Direction properties based on processing parameters and chemical composition, reducing the need for extensive physical testing.

Tailored microstructures with engineered grain boundaries and precipitate distributions represent the future direction for optimizing Cross Direction properties in advanced high-strength steels.