Wood Hardness Versus Moisture Content

Introduction

Figure 1: Wood Hardness Scale.

I have long been told that wood hardens as it ages, but I have anecdotal evidence that this is not always true. I also know that some species are far harder than others (Figure 1).

I read the following forum post that I thought presented really good information on wood hardness and moisture content that I would like to research a bit more and present here. The key point of the forum discussion was that wood gets harder as its moisture content decreases, which can happen to wood as it ages. Other factors, like insects and mold, will decrease the hardness of wood. I am only concerned with moisture here – the other factors are unpredictable.

I will present two numerical models for how the hardness of wood varies with moisture content. These two models will be shown to be roughly equivalent.

Background

Concept

There are many wood properties that vary with the moisture content of the wood. Here are a few examples:

hardness
shear modulus
tensile strength
compressive strength

I have seen two approaches to modeling the effect of moisture on these properties: (1) a power law relationship (USDA) and a linear model (Bozkurt Y, Göker Y [1987]). I will show that the two approaches produce similar results over a narrow moisture content range.

Definition of Hardness

My post here will focus on Janka hardness, which is a commonly used wood hardness measure. Here is the definition of the Janka measurement process and how moisture content is defined.

Janka Side Hardness

Janka side hardness is the load required to embed an 11.28-mm (0.444-in.) ball to one-half its diameter.

Moisture Content (M)

The percentage of wood mass consisting of water. It is often measured in the field using electrical test equipment. In the lab, it can be measured using by measuring the mass of a test sample before and after drying and computing $M\triangleq \frac{{{m}_{water}}}{{{m}_{dry}}}=\frac{{{m}_{wet}}-{{m}_{dry}}}{{{m}_{dry}}}$
where

m_water is the mass of water in the wood sample.
m_wet is the mass of the wood sample before drying.
m_dry is the mass of the dried wood sample.

Figure 2 illustrates the Janka test.

Figure 2: Illustration of the Janka Test (Wikipedia).

This post is focused on hardness, but the approach can be used for many other parameters.

Forest Products Laboratory Model (USDA)

Equation 1 shows the model from the Forest Products Laboratory (FPL). I will use data from the FPL to model wood hardness.

Eq. 1

$P(M)={{P}_{12}}\cdot {{\left( \frac{{{P}_{12}}}{{{P}_{g}}} \right)}^{\frac{\left( 12-M \right)}{\left( {{M}_{p}}-12 \right)}}}$

where

P a property of wood (e.g. hardness)
P₁₂ the property value at 12% moisture content.
P_g is the property value under green conditions.
M is the moisture content of the wood expressed as a percentage.
M_P is defined in Chapter 4 of the 1999 Wood Handbook as the moisture content percentage at the intersection of a horizontal line representing the strength of green wood and an inclined line representing the logarithm of the strength–moisture content relationship for dry wood. They then say to assume 25% if M_P is not known. I can explain why they say assume 25% if you do not have information otherwise. The intersection statement does not seem correct. I go into detail here.

Linear Model

Equation 2 shows a model that I have seen in many publications (example, sect 2.3) for normalizing data gathered from wood at various moisture contents to 12%, which is the industry standard for moisture content.

Eq. 2

$\displaystyle P\left( M \right)=\frac{{{P}_{12}}}{1+\alpha \cdot \left( M-12 \right)}\approx {{P}_{12}}\cdot \left[ 1-\alpha \cdot \left( M-12 \right) \right]$

where

P₁₂ is estimated value of a parameter at 12% moisture content.
P is measured value of a parameter at a moisture content of u%.
α is a constant that in general varies with the species of the wood under test. It can be calculated using $\displaystyle \alpha =\frac{\ln \left( \frac{{{H}_{12}}}{{{H}_{g}}} \right)}{{{M}_{p}}-12}$ . This relationship is derived in Figure 3.

Analysis

Objective

I will show how Equations 1 and 2 are related in that they produce similar results for wood hardness in the typical range of wood moisture contents.

Calculations

For my work here, I will work with the wood hardness normalized to the hardness at 12% moisture content. Normalizing allows me to work with numbers that are in the neighborhood of 1. Figure 3 shows my analysis.

Figure 3: Comparison of Exact and Linear Approximation.

Conclusion

I was able to show that Equations 1 and 2 produce similar results in the typical range of wood moisture contents (6% to 14%). I also see that the model states that wood gets harder as moisture content decreases, which is something that I have observed.

To centralize the data that I use for my personal work, I have included a list of the hardness parameters for common North American Species (Table 1).

Appendix A: M_P Values for Common North American Species.

M_P is an important parameter for estimating wood hardness and its value varies by species. The Wood Handbook states that its value is normally near 25%. Figure 4 shows some common M_P values and you can see that they are near 25%.

Figure 4: Table 4-13 from the Wood Handbook.

Appendix B: M_P Definition Discussion.

The definition of Equation 1 includes some phrasing that is difficult for me to figure out. I will try to provide some additional clarification here. Here is how M_P is defined.

M_P [is the] moisture content at the intersection of a horizontal line representing the strength of green wood and an inclined line representing the logarithm of the strength–moisture content relationship for dry wood.

I actually could not understand this statement as written, although I do think I can explain how you determine M_P. Figure 5 shows my explanation, which assumes you have (1) a plot of the hardness versus moisture content of the wood in question, and (2) you know the green hardness.

Figure 5: Explanation for Mp Determination Statement.

Figure 5 shows that the if we graph Equation 1, M_P is the moisture level at which the wood strength equals the green strength. Figure 6 illustrates the relationship between M_P and the Fiber Saturation Point (FSP). Observe that the "green" strength is reached before the FSP. This means that Equation 2 does not hold above M_P.

Figure 6: Relationship Between Mp and FSP.

Appendix C: Table of Hardness Values (Dry/Green/Ratio) for Common Species.

Table 1 is from a US Forest Service publication, which I have augmented with a column of common tree names. The scientific names are not of much use for me – I only know the common names of trees. Note that the hardness levels are specified in units of Newtons (metric measure) and there are 4.448 Newtons in a pound. For example, the hardness of Black Cherry is rated at 4210 Newtons, which is ~950 pounds.

Table 1: Hardness (Dry/Green) and Dry/Green Ratio By Species
Type	Common Name	Species	Dry Hard. (N)	Green Hard. (N)	Dry/Green Ratio
Hardwood	ALDER, COMMON	ALNUS GLUTINOSA	2940	2220	1.32
	ALDER, RED	ALNUS RUBRA	2620	1950	1.34
	ASH, BLACK	FRAXINUS NIGRA	3770	2310	1.63
	ASH, EUROPEAN	FRAXINUS EXCELSIOR	6140	4270	1.44
	ASH, GREEN	FRAXINUS PENNSYLVANICA	5320	3860	1.38
	ASH, OREGON	FRAXINUS LATIFOLIA	5140	3500	1.47
	ASH, WHITE	FRAXINUS AMERICANA	5850	4260	1.37
	ASPEN, QUAKING	POPULUS TREMULOIDES	1550	1330	1.17
	BEECH, AMERICAN	FAGUS GRANDIFOLIA	5760	3770	1.53
	BEECH, EUROPEAN	FAGUS SYLVATICA	6410	4270	1.50
	BIRCH, BLACK	BETULA LENTA	6520	4300	1.52
	BIRCH, PAPER	BETULA PAPYRIFERA	4040	2480	1.63
	BIRCH, YELLOW	BETULA ALLEGHANIENSIS	5590	3460	1.62
	BUTTERNUT	JUGLANS CINEREA	2170	1730	1.25
	CHERRY, BLACK	PRUNUS SEROTINA	4210	2930	1.44
	CHERRY, SWEET	PRUNUS AVIUM	5780	4140	1.40
	CHESTNUT, AMERICAN	CASTANEA DENTATA	2390	1860	1.28
	CHESTNUT, SWEET	CASTANEA SATIVA	3070	3160	0.97
	COTTONWOOD, BLACK	POPULUS TRICHOCARPA	1550	1110	1.40
	COTTONWOOD, EASTERN	POPULUS DELTOIDES	1910	1510	1.26
	CUCUMBERTREE	MAGNOLIA ACUMINATA	3100	2310	1.34
	GUM, BLACK	NYSSA SYLVATICA	3590	2840	1.26
	HACKBERRY, NORTHERN	CELTIS OCCIDENTALIS	3900	3100	1.26
	HONEYLOCUST	GLEDITSIA TRIACANTHOS	7010	6160	1.14
	HORNBEAM, EUROPEAN	CARPINUS BETULUS	6980	5470	1.28
	HORSE CHESTNUT	AESCULUS HIPPOCASTANUM	3340	2580	1.29
	MAGNOLIA, SOUTHERN	MAGNOLIA GRANDIFLORA	4520	3280	1.38
	MAPLE, BIGLEAF	ACER MACROPHYLLUM	3770	2750	1.37
	MAPLE, BLACK	ACER NIGRUM	5230	3730	1.40
	MAPLE, RED	ACER RUBRUM	4210	3100	1.36
	MAPLE, SILVER	ACER SACCHARINUM	3100	2620	1.18
	MAPLE, SUGAR	ACER SACCHARUM	6430	4300	1.50
	MAPLE, SYCAMORE	ACER PSEUDOPLATANUS	4850	3830	1.27
	OAK, AUSTRIAN	QUERCUS CERRIS	8270	6180	1.34
	OAK, SCARLET	QUERCUS COCCINEA	6210	5320	1.17
	OAK, SWAMP WHITE	QUERCUS BICOLOR	7180	5140	1.40
	OAK, WHITE	QUERCUS ALBA	6030	4700	1.28
	PECAN	CARYA ILLINOENSIS	8070	5810	1.39
	PLANETREE, LONDON	PLATANUS ACERIFOLIA	5650	4270	1.32
	POPLAR, TULIP	LIRIODENDRON TULIPIFERA	2390	1950	1.23
	SWEETGUM	LIQUIDAMBAR STYRACIFLUA	3770	2660	1.42
	SYCAMORE	PLATANUS OCCIDENTALIS	3410	2710	1.26
	TUPELO, WATER	NYSSA AQUATICA	3900	3150	1.24
	WALNUT, BLACK	JUGLANS NIGRA	4480	3990	1.12
	WALNUT, PERSIAN	JUGLANS REGIA	3600	2970	1.21
	POPLAR, CANADIAN	POPULUS CANADENSIS	2220	2050	1.08
	POPLAR, SILVER	POPULUS CANESCENS	2360	1730	1.36
Hardwood Average			4474	3343	1.34
Softwood	BALDCYPRESS	TAXODIUM DISTICHUM	2260	1730	1.31
	CEDAR, ALASKA	CHAMAECYPARIS OOTKATENSIS	2570	1950	1.32
	CEDAR, ATLANTIC WHITE	CHAMAECYPARIS THYOIDES	1550	1290	1.20
	CEDAR, PORT ORFORD	CHAMAECYPARIS LAWSONIANA	2790	1690	1.65
	FIR, BALSAM	ABIES BALSAMEA	1770	1290	1.37
	FIR, CALIFORNIA RED	ABIES MAGNIFICA	2220	1600	1.39
	FIR, DOUGLAS	PSEUDOTSUGA MENZIESII	2930	2260	1.30
	FIR, GRAND	ABIES GRANDIS	2170	1600	1.36
	FIR, NOBLE	ABIES PROCERA	1820	1290	1.41
	FIR, PACIFIC SILVER	ABIES AMABILIS	1910	1380	1.38
	FIR, SILVER	ABIES ALBA	2850	1910	1.49
	FIR, SUBALPINE	ABIES LASIOCARPA	1550	1150	1.35
	FIR, WHITE	ABIES CONCOLOR	2130	1510	1.41
	HEMLOCK, EASTERN	TSUGA CANADENSIS	2220	1770	1.25
	HEMLOCK, MOUNTAIN	TSUGA MERTENSIANA	3020	2080	1.45
	HEMLOCK, WESTERN	TSUGA HETEROPHYLLA	2390	1820	1.31
	INCENSE CEDAR	LIBOCEDRUS DECURRENS	2080	1730	1.20
	LARCH, EUROPEAN	LARIX DECIDUA	3770	2450	1.54
	LARCH, JAPANESE	LARIX KAEMPFERI	2940	2140	1.37
	LARCH, WESTERN	LARIX OCCIDENTALIS	3680	2260	1.63
	PINE, AUSTRIAN	PINUS NIGRA	2890	1910	1.51
	PINE, CLUSTER	PINUS PINASTER	2670	1690	1.58
	PINE, EASTERN WHITE	PINUS STROBUS	1690	1290	1.31
	PINE, JACK	PINUS BANKSIANA	2530	1770	1.43
	PINE, LOBLOLLY	PINUS TAEDA	3060	2000	1.53
	PINE, LODGEPOLE	PINUS CONTORTA	2130	1460	1.46
	PINE, LONGLEAF	PINUS PALUSTRIS	3860	2620	1.47
	PINE, MONTEREY	PINUS RADIATA	3330	2130	1.56
	PINE, PONDEROSA	PINUS PONDEROSA	2040	1420	1.44
	PINE, RED	PINUS RESINOSA	2480	1510	1.64
	PINE, SCOTCH	PINUS SYLVESTRIS	2980	2220	1.34
	PINE, SHORTLEAF	PINUS ECHINATA	3060	1950	1.57
	PINE, SPRUCE	PINUS GLABRA	2930	2000	1.47
	PINE, SUGAR	PINUS LAMBERTIANA	1690	1200	1.41
	PINE, VIRGINIA	PINUS VIRGINIANA	3280	2390	1.37
	PINE, WESTERN WHITE	PINUS MONTICOLA	1860	1150	1.62
	REDCEDAR, EASTERN	JUNIPERUS VIRGINIANA	4000	2880	1.39
	REDCEDAR, WESTERN	THUJA PLICATA	1550	1150	1.35
	REDWOOD, COAST	SEQUOIA SEMPERVIRENS	2130	1820	1.17
	SPRUCE, BLACK	PICEA MARIANA	2310	1640	1.41
	SPRUCE, ENGELMANN	PICEA ENGELMANNII	1730	1150	1.50
	SPRUCE, NORWAY	PICEA ABIES	2110	1420	1.49
	SPRUCE, RED	PICEA RUBENS	2170	1550	1.40
	SPRUCE, SERBIAN	PICEA OMORIKA	2710	1470	1.84
	SPRUCE, SITKA	PICEA SITCHENSIS	2260	1550	1.46
	TAMARACK	LARIX LARICINA	2620	1690	1.55
	WHITE CEDAR, NORTHERN	THUJA OCCIDENTALIS	1420	1020	1.39
Softwood Average			2470	1722	1.43
Grand Average			3472	2533	1.38

Wood Hardness Versus Moisture Content

Introduction